IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE
?INOEOOO IAOAIAOEEE
AeAEAOeUeEEE Ieaen?e TH??eiae/
OAeE 513.88
AeEOA?AIOe?AEUeI?
OA
INAAAeIAeEOA?AIOe?AEUeI?
IIA?AOI?E
IA
IANE?I*AIIIAEI??IEO
IIIAIAEAeAO
01.01.01 – iaoaiaoe/iee aiae?c
AAOI?AOA?AO
aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy
aeieoi?a o?ceei-iaoaiaoe/ieo iaoe
Ee?a 1999
Aeena?oaoe??th ? ?oeiien.
?iaioo aeeiiaii a ?inoeooo? iaoaiaoeee IAI Oe?a?ie
Iaoeiaee eiinoeueoaio:
aeaaeai?e IAI Oe?a?ie,
aeieoi? o?ceei-iaoaiaoe/ieo iaoe
AA?ACAINUeEEE TH??e Iaea?iae/,
?inoeooo? iaoaiaoeee IAI Oe?a?ie,
caa?aeoaa/ a?aeae?eo
Io?oe?ei? iiiiaioe:
/eai-ei?aniiiaeaio IAI Oe?a?ie, aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
IAO?EIA Aeieo?i sseiae/, ?inoeooo? iaoaiaoeee IAI Oe?a?ie,
caa?aeoaa/ a?aeae?eo
/eai-ei?aniiiaeaio IAI Oe?a?ie, aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
ssAe?AIEI Ieoaeei Eineiiae/, Ee?anueeee iaoe?iiaeueiee oi?aa?ne-
oao ?i. Oa?ana Oaa/aiea, i?ioani?
aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
NIIEssIIA Ieaa Aai?a?eiae/, Iineianueeee aea?aeaaiee oi?aa?ne-
oao ?i. I.A.Eiiiiiniaa, ?in?y, i?ioani?
I?ia?aeia onoaiiaa: O?ceei-oaoi?/iee ?inoeooo iocueeeo oaiia?aoo? ?i.
A.?.A??e?ia IAI Oe?a?ie
Caoeno a?aeaoaeaoueny 1 /a?aiy 1999 ?ieo i 15 aiaeei?
ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.206.01
i?e ?inoeooo? iaoaiaoeee IAI Oe?a?ie ca aae?anith:
252601 Ee?a 4, INI, aoe. Oa?auaie?anueea, 3
C aeena?oaoe??th iiaeia iciaeiieoenue a a?ae?ioaoe?
?inoeoooo iaoaiaoeee IAI Oe?a?ie
Aaoi?aoa?ao ?ic?neaii 27 ea?oiy 1999 ?ieo.
A/aiee nae?aoa?
niaoe?ae?ciaaii? a/aii? ?aaee
aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
i?ioani?
Ia?aaa?c?a N.A.
CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE
Aeooaeueiinoue oaie
Oai??y aeeoa?aioe?aeueiex oa inaaaeiaeeoa?aioe?aeueiex iia?aoi??a, ui
ae?thoue o i?inoi?ax ooieoe?e iane?i/aiii? e?eueeino? ci?iiex, ? iaeiei
?ciaeaaaeeea?oex ?icae?e?a iane?i/aiiiaei??iiai aiae?co. C iaeiiai aieo,
neeueiith iioeaaoe??th ?icaeoeo oe??? aaeoc? ? canoinoaaiiy o
iaoaiaoe/i?eoa oai?aoe/i?e o?ceoe?. C ae?oaiai aieo, oeae ?icaeoie
aeiaaa? canoinoaaiiy ?aeae oa iaoiae?a aaiiao???, oiiieia??, oai???
i??e, oai??? iia?aoi??a, ui aea? yne?aaee i?eeeaae ?ioa?iieyoe?? ??ciex
aaeocae iaoaiaoeee. Oae? iia?aoi?e ?icaeyaeaeenue o ?iaioax aaaaoueix
aaoi??a (N.Aeueaaaa??i, .I.Aa?acainueeee, O.I.Aa?ac?i, I.A?oee,
?.I.Aaeueoaiae, E.A?inn, TH.A.Eiiae?aoue?a, I.?ueieia?, I.A.Niieyiia,
I.TH.O?aii?eia oa
iaoe?ia oice/ia eioa?aoo?a). A?eueoa /anoeia ?nioth/eo ?ia?o i?enay/aia
aeiaaeeo e?i?eiiai oaciaiai i?inoi?o. Aeiaaeie iae?i?eiex oaciaex
i?inoi??a a?ae?a?a? ia iaio aaaeeeao ?ieue o iaoaiaoe/iiio aiae?c? oa
iaoaiaoe/i?e o?ceoe?
(iai?eeeaae, o eaaioia?e oai??? iiey oa noaoenoe/i?e o?ceoe?). Ia?ax?ae
aei oeueiai aeiaaeeo i?ecaiaeeoue aei aaaaoueix o?oaeiiu?a o ca’yceo ?c
neeaaeiith
aaiiao?e/iith no?oeoo?ith iane?i/aiiiaei??iex iiiaiaeae?a, ye?
i?e?iaeiuei c’yaeythoueny o canoinoaaiiyx, oa a?aenooi?no? caaaeueii?
oai??? oaeex iiiaiaeae?a. Oiio aeine?aeaeaiiy eiaeiiai i?eeeaaeo oaeiai
oeio aeiaaa? ?icaeoeo iniaeeai? oaxi?ee.
Oe?eaaei oa aaaeeeaei eeanii aeeoa?aioe?aeueiex iia?aoi??a ia
iane?i/aiiiaei??iex iiiaiaeaeax ? iia?aoi?e Ae???xea, anioe?eiaai? c
a?aan?anueeeie i??aie ia iane?i/aiiex aeiaooeax eiiiaeoiex ?eiaiiaex
iiiaiaeae?a. Oae? iia?aoi?e c’yaeythoueny o ca’yceo c a?ao/anoeie
iiaeaeyie noaoenoe/ii? iaxai?ee. ??ci? aniaeoe aeine?aeaeaiiy oeex
iia?aoi??a oa a?aeiia?aeiex i?aa?oi ?icaeyaeaeenue aaaaoueia aaoi?aie
(Ae.No?oe, A.Caaa?eeinueeee, N.Aeueaaaa??i, TH.A.Eiiae?aoue?a,
I.?ueieia? oa ?io?).
Caoaaaeeii, ui o aeiaaeeo e?i?eiiai ni?iiaiai i?inoi?o
noixanoe/ia aeeiai?ea, ui a?aeiia?aea? a?aan?anuee?e i???, iiaea aooe
iiaoaeiaaia ??cieie niiniaaie (iaoiae oi?i Ae???xe?, aaciina?aaeiy
iia?aoi?ia eiino?oeoe?y ia?e?anueei? i?aa?oie ?c caaeaiei aaia?aoi?ii oa
i?aex?ae, ui aeei?enoiao? noixanoe/i? aeeoa?aioe?aeuei? ??aiyiiy). O
aeiaaeeo eiiiaeoiex ni?iiaeo i?inoi??aia?o? aeaa i?aexiaee aeia?a
?icaeiai?. Cie?aia, aaciina?aaeiy eiino?oeoe?y i?aa?oie, ui aeei?enoiao?
yaiee aeaeyae aaia?aoi?a, aea?oueny o ?iaioax Ae.No?oea ?
A.Caaa?eeinueeiai. I?ioa i?yia iiaoaeiaa a?aeiia?aeiiai i?ioeano ca
aeiiiiiaith oai??e noixanoe/iex aeeoa?aioe?aeueieo ??aiyiue (“aeaoaa?iaa
aeeiai?ea”), ui aea? e?auee eiio?ieue eiai aeanoeainoae, cono??/a?oueny
c na?eicieie o?oaeiiuaie oa aeiaaa? ?icaeoeo a?aeiia?aeii? aiae?oe/ii?
oaxi?ee. O iaei?ino?oiio aeiaaeeo iane?i/aiiiaei??iiai oi?o oaeee
i?aex?ae aoa ?aae?ciaaiee ?.Oiee? oa Ae.No?oeii. Ia?ax?ae aei aeiaaeeo
iao?ea?aeueiex eiiiaeoiex iiiaiaeae?a i?ecaiaeeoue aei aaaaoueix
aeiaeaoeiaex o?oaeiiu?a. Oiio, iacaaaeath/e ia aaeeeo e?euee?noue ?iaio
o oeueiio iai?yieo, oeae aeiaaeie caeeoeany iaaeine?aeaeaiiei.
Cacia/eii, ui a?aenooi?noue no?oeoo?e aeaaeeiai a?eue?a?oiaa aai
aaiaxiaa iiiaiaeaeo ?iaeoue iaiiaeeeaei aeei?enoaiiy ?nioth/i? oai???
noixanoe/iex aeeoa?aioe?aeueiex ??aiyiue (NAe?) ia iane?i/aiiiaei??iex
iiiaiaeaeax. Oiio ia?oei e?ieii o iai?yieo ?aae?caoe?? i?ia?aie
“noixanoe/iiai
eaaiooaaiiy” ia i?iaeaeo-iiiaiaeaeax ? ?icaeoie iaiax?aeii?
aeeoa?aioe?aeueii-aaiiao?e/ii?
oaxi?ee oa a?aeiia?aeii? oai??? NAe?.
Aaaeeeaei iaoiaeii aeine?aeaeaiiy aeeoa?aioe?aeueiex iia?aoi??a ?
oae caaia neiaieueia /eneaiiy. Oea icia/a?, ui aeeoa?aioe?aeueiee
iia?aoi? ?icaeyaea?oueny ye ooieoe?y a?ae “aeaiaioa?iex” iia?aoi??a
iiiaeaiiy oa aeeoa?aioe?thaaiiy. ?icaeoie oeueiai /eneaiiy aaaea aei
oai??? inaaaeiaeeoa?aioe?aeueiex iia?aoi??a (IAeI). Oaeei /eiii, eean
IAeI ?, c iaeiiai aieo, i?e?iaei?i ?icoe?aiiyi eeano aeeoa?aioe?aeueiex
iia?aoi??a, oa c ?ioiai aieo, iniaenoi a?ae?a?a? aaaeeeao ?ieue o
canoinoaaiiyx. Aeiaaeie ne?i/aiiiaei??iex oaciaex i?inoi??a aea/aany
aaaaoueia aaoi?aie, cie?aia o eeane/iex ?iaioax A.I.Ianeiaa oa
E.Xuei?iaiaea?a. Iiooaeiei caniaii aea/aiiy aneiioioe/ii? iiaaae?iee
IAeI ? iaoiae eaiii?/iiai iia?aoi?a Ianeiaa, yeee aea? iiaeeea?noue
anoaiiaeoe ca’ycie aneiioioe/iex ?ica’yce?a inaaaeiaeeoa?aioe?aeueiex
??aiyiue c aaiiao???th eaa?aiaeiaex iiiaiaeae?a, ui iienothoueny
?ica’yceaie a?aeiia?aeiex aai?eueoiiiaex nenoai. Iiaeaeueoee ?ica’ycie
oeueiai iaoiaeo aea? iiaeeea?noue iiaoaeiae aneiioioe/iex ?ica’yce?a
inaaaeiaeeoa?aioe?aeueiex ??aiyiue O?aae?iaa?a, ye? a naith /a?ao
aeei?enoiaothoueny o eiino?oeoe?? IAeI c iae?i?eieie
oaciaeie i?inoi?aie.
?aae?caoe?y oaei? i?ia?aie o iane?i/aiiiaei??iiio aeiaaeeo ?
aeoaea aaaeeeaith oa o?oaeiith caaea/ath. Aeaye? eiie?aoi? eeane
iane?i/aiiiaei??iex IAeI ?icaeyaeaeenue o ?iaioax O.I.Aa?aciia,
I.Aioeea, I.A.Niieyiiaa, I.TH.X?aiiieiaa, aea ?icaeiaia o oeex ?iaioax
oaxi?ea nooo?ai aeei?enoiao? e?i?eio no?oeoo?o oaciaiai i?inoi?o. A?eueo
oiai, ni?iae iiaoaeoaaoe iane?i/aiiiaei??iee eaiii?/iee iia?aoi? Ianeiaa
cono??/athoueny c na?eicieie o?oaeiiuaie, ui iia’ycai? c aaiiao???th
iane?i/aiiiaei??iex eaa?aiaeiaex oa neiieaeoe/iex iiiaiaeae?a. Oaeei
/eiii, iaa?oue iiaoaeiaa eiie?aoiex i?eeeaae?a iane?i/aiiiaei??iex
iiiaiaeae?a oa aeaaa? neiaie?a, aeey yeex oey i?ia?aia ? ?aae?noe/iith,
? aeoaea aaaeeeaei caaaeaiiyi.
Oaeei /eiii, aaeeeee ?ioa?an aei oai??? aeeoa?aioe?aeueiex oa
inaaaeiaeeoa?aioe?aeueiex iia?aoi??a c iae?i?eieie iane?i/aiiiaei??ieie
oaciaeie i?inoi?aie, oa ?? ca’ycie ?c /eneaiieie no/anieie o?ce/ieie
oai??yie, oaeeie ye oai??y noixanoe/iiai eaaiooaaiiy eaaioiaex oa
eeane/iex a?ao/anoex iiaeaeae, oai??y aneiioioe/iiai eaaiooaaiiy,
?iaeoue oaio aeena?oaoe?? aeoaea aeooaeueiith.
Ca’ycie c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.
?iaioo aeeiiaii ca?aeii c iaoeiaeie oaiaie oa ieaiaie Iinoeoooo
iaoaiaoeee IAI Oe?a?ie. (? aea?aeaaii? ?a?no?aoe?? – 0198U001995).
Iaoa ?iaioe.
Iaoith ?iaioe ? aea/aiiy aeayeex eeania aeeoa?aioe?aeueiex oa
inaaaeiaeeoa?aioe?aeueiex iia?aoi?ia ia ianeii/aiiiaeii?iex iiiaiaeaeax,
a naia iia?aoi??a Ae???xea a?anianueeex ii? ia ianeii/aiiex aeiaooeax
eiiiaeoiex iiiaiaeaeia oa inaaaeiaeeoa?aioe?aeueieo iia?aoi??a c
neiaieaie ia a?eueaa?oiaeo neiieaeoe/ieo i?inoi?ao ? iiiaiaeaeao,
cie?aia, iiiaiaeaeax ?ica‘yce?a iane?i/aiiiaei??ieo aaiieueoiiiaex
nenoai.
Iaoiaeeea aeineiaeaeaiiy.
O ?iaioi aeei?enoiaothoueny iaoiaee ooieoeiiiaeueiiai aiaeico,
oai?i?
noixanoe/iex aeeoa?aioe?aeueiex ?iaiyiue oa aeeoa?aioe?aeueii?
aaiiao?i?.
Iaoeiaa iiaecia iaea?aeaiex ?acoeueoaoia.
Iniiaieie ?acoeueoaoaie, ui aecia/athoue iaoeiao iiaecio ?iaioe
oa aeiinyoueny ia caoeno, ? ianooii? ?acoeueoaoe:
1. Iiaoaeiaaii eiiai?i?nii i?aaenoaaeaiiy i?aa?oi, ui ii?iaeaeaii
iia?aoi?aie
Ae???xea oe?ieiai eeano a?aan?anueeex ii? ia ianeii/aiiex aeiaooeax
eiiiaeoiex iiiaiaeaeia, oa aeiaaaeaii ?o oaea?ia?noue.
Ca aeiiiiiaith oeeo i?aaenoaaeaiiue aeiaaaeaii nooo?ao
naiini?yaeaiinoue
oaeex iia?aoi?ia Ae???xea o ?aci
ianeii/aiiiai ?aiao aca?iiaeie oa io?eiaii iien aeno?aiaeueiex
a?aan?anueeex ii? ia ianeii/aiiex aeiaooeax
eiiiaeoiex iiiaiaeaeia o oa?iiiax a?aiaee/iinoi aiaeiiaiaeii?
noixanoe/ii?
aeeiaiiee.
2. Aeiaaaeaii inioaaiiy oa ?aeeiinoue neeueieo
?ica’yce?a ianeii/aiiex nenoai noixanoe/iex
aeeoa?aioe?aeueiex ?iaiyiue ia eiiiaeoiex iiiaiaeaeax. Aeiaaaeaii
eaaciiiaa?iaioiinoue ?iciiaeieia ?ica’yce?a oaeex nenoai ia a?oiao E?.
3. ?ic?iaeaii eiino?oeoeith IAeI c neiaieaie ia aieueaa?oiaiio
oaciaiioi?inoi?i, ui aeithoue o L_2 ii aeaaeeie ii?i ia aieueaa?oiaiio
i?inoi?i.
Aeiaaaeaii iniiaii aneiioioe/ii oi?ioee neiaieueiiai /eneaiiy oaeex
iia?aoi?ia, cie?aia oi?ioee eiiooaoe?? oa eiiiiceoe??.
4. Iiaoaeiaaii aneiioioe/ii ?ica’ycee aiaeiiaiaeiex
inaaaeiaeeoa?aioe?aeueiex?iaiyiue O?aaeiiaa?a.
5. Iiaoaeiaaii aeaaa?o IAeI c neiaieaie ia i?eionoeiex neiieaeoe/iex
iiiaiaeaeax, cie?aia, iiiaiaeaeax ?ica’yce?a iane?i/aiiiaei??ieo
aaiieueoiiiaex nenoai.
6. Iia?aoi? Ae???xea aaonniai? ii?e ia aieueaa?oiaiio i?inoi?i
?aaeiciaaiiye aeaiaio aeaaa?e IAeI; aeiaaaeaii aiaeiiaiaeii aneiioioe/ii
oi?ioee
neiaieueiiai /eneaiiy.
7. ?icaeiooi iiai aaiiao?e/ii iaoiaee ?ica’ycoaaiiy aeayeex eeane/iex
aaiieueoiiiaex nenoai, ui ocaaaeueiththoue noaio Einoaioa-Aaeea?a.
Oai?aoe/ia cia/aiiy.
?acoeueoaoe oa iaoiaee, ui ?ic?iaeaii o aeena?oaoei?, aeoeaii
aeei?enoiaothoueny
o iiaeaeueoex aeineiaeaeaiiyx a iaeanoi oai??? aeeoa?aioe?aeueiex oa
inaaaeiaeeoa?aioe?aeueiex iia?aoi?ia ia ianeii/aiiiaeii?iex iiiaiaeaeax
oa ?x canoinoaaiue. Aiie iiaeooue aooe ei?enieie o iaoeiaie ?iaioi
Iinoeoooo iaoaiaoeee IAI Oe?a?ie, Ee?anueeiai aea?aeaaiiai oi?aa?neoaoo,
O?ceei-oaoi?/iiai ?inoeoooo iecueeeo
oaiia?aoo?,
Iineianueeiai iinoeoooo aeaeo?iiiee oa iaoaiaoeee, oi?aa?neoao?a i?no
Aiiia (Iiia//eia), Oi?aiea (Aaeeeia?eoaiiy), Iaini (O?aioeiy).
Iniaenoee aianie caeiaoaa/a.
Iniiaii ?acoeueoaoe aeena?oaoei? io?eiaii aaoi?ii naiinoieii. Aeeaae
eiaeiiai
ic niiaaaoi?ia /ioei aeaeieaii a aeena?oaoe?eiie ?iaioi.
Ai?iaaoeiy ?acoeueoaoia.
Iaoa?iaee aeena?oaoei? aeiiiaiaeaeenue oa iaaiai?thaaeenue ia 5-io
?a?iiaenueeiio
Neiiicioii ?c noixanoe/iiai aiaeico (Aiii, Iiia//eia, 1994),
Iiaeia?iaeiie
eiioa?aioei? “Iaoiaee noixanoe/iiai aiaeico o noixanoe/iie iaxaiioei,
oiiainax oa aiieiai?” (Aieaoaeueae, Iiia//eia, 1994), Iiaeia?iaeiie
eiioa?aioei? ?c noixanoe/iiai aiaeico oa eiai canoinoaaiue (Ia?naeue,
O?aioeiy, 1995), Iiaeia?iaeiiio naiano?i “Ooieoeiiiaeueia iioaa?oaaiiy”
(Ia?eae, O?aioeiy, 1997), Iiaeia?iaeiie eiioa?aioei? “Noixanoe/ii Aeii
98” (Ithixai, Iiia//eia, 1998), Iiaeia?iaeiie eiioa?aioei? c
iaoaiaoe/ii? oiceee (Einaaii, Ii?ooaaeiy, 1998), Iiaeia?iaeiie
eiioa?aioei? c iioaioeiaeueiiai aiaeico (Ooiin, 1998), naiiia?ax
Iinoeoooo iaoaiaoeee IAI Oe?a?ie, O?ceei-oaoi?/iiai ?inoeoooo iecueeeo
oaiia?aoo? oa iaoaiaoe/iex oaeoeueoaoia
oiiaa?neoaoia Aiiia, Aixoia, Aieaoaeueaea, Iiooiiaaia, Oi?aiea oa Xaeea.
Ioaeieaoei?.
Ca iaoa?iaeaie aeena?oaoei? iioaeieiaaii 16 iaoeiaex ?iaio.
Ia’?i oa no?oeoo?a.
Aeena?oaoe?y aeeeaaeaia ia 266 noi??ieao oa neeaaea?oueny c anooio,
3 ?icae?e?a, aeniiae?a oa nieneo oeeoiaaii? e?oa?aoo?e, ui i?noeoue 118
aeaea?ae.
INIIAIEE CIINO ?IAIOE
?icae?e 1 i?enay/aiee aea/aiith iia?aoi??a Ae???oea, ui iia’ycai? c
a?aan?anueeeie i??aie ia (iane?i/aieo) i?iaeaeo-iiiaiaeaeao. O
I?ae?icae?e? 1.1 ie iaaiai?th?ii iniiai? aaiiao?e/i? no?oeoo?e oa
?icaeaa?ii noioanoe/ia /eneaiiy ia (iane?i/aiieo) i?iaeaeo-iiiaiaeaeao.
O Ioieo? 1.1.1 ie aaiaeeii iniiai? ia’?eoe ia iicia/aiiy.
Iaoae M — eiiiaeoiee ??iai?a iiiaiaeae. Ie iicia/a?ii /a?ac d_Xu
iio?aeio ooieoe?? u ocaeiaae aaeoi?iiai iiey X. A?aeiia?aeiee a?aae??io,
aecia/aiee ca aeiiiiiaith ??iaiiai? no?oeoo?e (cdot ,cdot ),
iicia/a?oueny /a?ac nabla u. A?aeiia?aeia a?aenoaiue ia M iicia/a?oueny
/a?ac rho. Ie ?icaeyaea?ii oe?eo a?aoeo bf Z^d,,dge 1, oa aecia/a?ii
i?ino?? bf Mequiv M^bf Z^d (yeee aoaeaii iaceaaoe i?iaeaeo-iiiaiaeaeii).
O Ioieo? 1.1.2 ie aoaeo?ii aeioe/ia ?icoa?oaaiiy Tbf M oa aecia/a?ii ca
eiai aeiiiiiaith aeeoa?aioe?aeuei? oa iao?e/i? no?oeoo?e ia bf M.
Caoaaaeeii, ui i?ino?? bf M ia? no?oeoo?o aaiaoiaiai iiiaiaeaeo
(iiaeaeeth yeiai ? i?ino?? iaiaaeaieo iine?aeiaiinoae ?c ??aiii??iith
ii?iith). Oey ii?ia ia ? aeeoa?aioe?eiaiith, ui ia aea?
iiaeeeaino? aeei?enoiaoaaoe oeth no?oeoo?o iiiaiaeaea aeey iiaoaeiae
noioanoe/iiai aiae?co. C iaoith iiaeieaiiy oe??? ia?aoeiaee, ie aaiaeeii
aiaeia ??iaiiai? no?oeoo?e ia bf M. Ia aa?enoe/iiio ??ai? aeioe/ia
?icoa?oaaiiy Tbf M ? bf Z^d-nooiaiai TM. I?e?iaeii ?icaeyiooe aeayea
a?eueaa?oiaa i?ae?icoa?oaaiiy oeueiai i?inoi?o. Cao?eno?ii aaaiao
iine?aeiai?noue pin l_1 aeiaeaoieo /enae oa aecia/eii a?eueaa?o?a
i?ino??
bf T_p,x=left Xin T_xbf M:sum_kin bf Z^dp_kleft|
X_kright| ^2
aea
?icaeyiaii aeiaaeie, eiee aeai?no?noue cal K oa cal K^prime ?
ii?iaeaeaiith neaey?iei aeiaooeii a?eueaa?oiaiai i?inoi?o cal K _0,
cal Ksubset cal K_0subset cal K^prime .
I?iiiceoe?y 1.4.
I?aa?oia bf T^xi ,eta(t) caaeiaieueiy? ianooiio ioe?ieo:
left| bf T^xi ,eta (t)v(x)right| _cal K^prime le
e^tc,T^xi (t)left| vright| _cal K^prime (x),
aea vin C(bf Mrightarrow cal
K^prime ) oa c oaea, ui ccdot (h,h)_cal Kge
2(b(x)h,h)_cal K+Tr_cal H(B(x)hcdot ,B(x)hcdot )_cal K
aeey aeia?eueieo xin bf M oa hin cal K.
Caoaaaeaiiy.
Iaoae ?nio? c_0 oaea, ui
ccdot (h,h)_cal K_0ge 2(b(x)h,h)_cal K_0+Tr_cal H
(B(x)hcdot ,B(x)hcdot )_cal K_0
aeey aeia?eueieo xin bf M oa hin cal K. Oiae? ie ia?ii ioe?ieo
sf Eleft| eta
(t)right| _cal K_0le e^c_0tsf Eleft| eta _0(0)right|
_cal K_0^2.
Aiane?aeie oeueiai bf T^xi ,eta (t) ae?? o i?inoi?? C(bf Mrightarrow cal
K_0), oa aeey vin C(bf Mrightarrow cal K_0) ie ia?ii
left| bf T^xi ,eta (t)v(x)right| _cal K_0le
e^tc_0,T^xi (t)left| vright| _cal K_0(x).
I?iiiceoe?y 1.5.
Iaoae ain C^2(bf M_prightarrow Tbf M_p),
Ain C^3(bf M%_prightarrow HS(cal H,Tbf M_p)),
oa, aeey aeia?eueiiai yin cal K, b(cdot )yin C^1(bf M_prightarrow cal
K),
B(cdot )yin C^1(bf M%_prightarrow HS(cal H,cal K))
??aiii??ii uiaei y. Oiae? a?aeia?aaeaiiy
bf M_pbf ni xlongmapsto (xi _x(t),eta _x(t))in bf M_ptimescal K
? aeeoa?aioe?eiaiei o na?aaeiuei-eaaae?aoe/iiio nain?.
Iane?aeie.
I?e oiiaao iiia?aaeiuei? i?iiiceoe??, i?aa?oia
bf T^xi ,eta (t)
caeeoa? ?iaa??aioiei i?ino?? C^1(bf M_prightarrowcal K^prime ).
Aiaeia?/ii iiaeia aeiaanoe, ui aiia caeeoa? ?iaa??aioieie an? i?inoi?e
C^s(bf M_prightarrow cal K^prime ),,sle k, yeui eiao?oe??ioe a,b,B
(a?aeiia?aeii A) ? k (a?aeiia?aeii k+1) ?ac?a aeeoa?aioe?eiaieie.
O I?ae?icae?e? 1.3 ie ?icaeyaea?ii aeiaaeie, eiee M=G ia? no?oeoo?o
a?oie E?.
Ie aaiaeeii nenoaio e?ai-?iaa??aioiex NAe? o oi?i? No?aoiiiae/a ia G:
dxi _k(t)=L_xi _k(t)[a_k(xi (t))dt+circ dw_k(t)],;kin bf Z^d,
labeliqi2
aea w_k — iacaeaaei? a?ia??anuee? i?ioeane o cal G (a?aeiia?aei?e
aeaaa?? E?), a_k — caaeai? a?aeia?aaeaiiy G^bf Z ^drightarrow cal G,
oa L_g iicia/a? e?aee cnoa
ia aeaiaio gin G. Ie aea/a?ii oeth nenoaio ca aeiiiiiaith iaoiae?a,
?icaeyiooeo aeua. Ie i?eionea?ii, ui:
left( iright) ;
sup_kin bf Z^dsup_xin G^bf Z^d
left| a_k(x)right| _cal G
Iaoae H ? ooieoe??th (neiaieii) ia cal H_-^2. Aecia/eii
inaaaeiaeeoa?ai-oe?aeueiee iia?aoi? (IAeI) H(x,ihbar D_mu ) a L_2(cal
H_-,mu ) ca aeiiiiiaith oi?ioee
H(x,ihbar D_mu )varphi (x)=F_pto x^-1F_yto p[H(fracx+y2,hbar
p)varphi (y)], labelif12
hbar in (0,1]. Acaaae? oey oi?ioea ia? o?eueee aa?enoe/iee nain. Aeae?
ie aeiaaaeaii, ui oeae ae?ac ? ei?aeoiei aeey eiie?aoieo eean?a neiaie?a
ia eiie?aoieo iaeanoyo aecia/aiiy.
O Ioieo? 2.2.2 ie ?icaeaa?ii neiaieueia /eneaiiy aeey IAeI c neiaieaie,
ye? ? ia?aoai?aiiyie Oo?’? iaiaaeaieo eiiieaeniicia/ieo i??. Ie
aeei?enoiao?ii
iiiyooy ?ioaa?aeo ooieoe??, yea i?eeia? cia/aiiy o aaiaoiaiio i?inoi??,
a?aeiinii i??e iaiaaeaii? aa??aoe??. Nii/aoeo ie aea?ii ?ioa aecia/aiiy
IAeI. Aeey Hin cal F_infty equiv cal F_infty (cal H_-^2,bf C^1)
(i?ino?? ooieoe?e, ye? ? ia?aoai?aiiyie Oo?’? eiiieaeniicia/ieo
iaiaaeaieo aeaaeeeo i?? ia cal H_+^2),
H(x,p)=int e^?( )dmu _H(x^prime,p^prime ), ie aecia/a?ii widehatH=int W_fracx^prime 2U_hbar p^prime W_fracx^prime 2dmu _H(x^prime ,p^prime ), labelin1 aea W_yphi :=e^ Oaa?aeaeaiiy 2.1. Oi?ioea (refin1) aecia/a? iia?aoi? widehatH a L_2(cal H_-,mu ) oa widehatHf(x)=F_pto x^-1F_yto p[H(fracx+y2,hbar p)f(y)]. labelin3 Oaa?aeaeaiiy 2.2. Iaoae H,Gin cal F_infty , H(x,p)=int e^? dtheta _H(x^prime ,p^prime ). Oiae?: widehatHwidehatG=widehatN_1, widehatGwidehatH=widehatN_2, aea N_1,N_2in cal F_infty oa N_1(x,p)=int e^? G(x+hbar p^prime /2,p-hbar x^prime /2)dtheta _H(x^prime ,p^prime ), labelif22 N_2(x,p)=int e^? G(x-hbar p^prime /2,p+hbar x^prime /2)dtheta _H(x^prime ,p^prime ). labelif23 Iane?aeie 2.1. Oi?ioea eiiooaoe??. Iaxae G,Hin cal F_infty . Oiae? frac ihbar [widehatH,widehatG]=widehatH,G+O(hbar ^2), labelif24 aea cdot ,cdot iicia/a? noaiaea?oio aeoaeeo Ioanniia ia cal H^2, yea aecia/a?oueny ca aeiiiiiaith ae?aco left H,Gright =leftlangle fracpartial Hpartial x,frac partial Gpartial prightrangle -leftlangle fracpartial G partial x,fracpartial Hpartial prightrangle. Caeeoie ia? oi?io hbar ^2widehatR(hbar ) c R(hbar )in cal F_infty ,;left| R(hbar )right| _cal F_lambda ? iaiaaeaiith ??aiii??ii a?aeiinii hbar aeey aoaeue-yeiai lambda in bf _+. Ie aea?ii oaeiae ?ioo ?ioa?i?aoaoe?th oi?ioee eiiiiceoe??. Aeey oeueiai IAeI ?ioiai oeio. sseui Hin cal F_infty , iia?aoi? H(x,ihbar partial H(x,ihbar partial /partial x)varphi (x)=int^sim e^-frac ihbar H(x,p)varphi (y)dpdy labelif25 (I.A.Niieyiia, I.TH.X?aii?eia). Neiaie int^sim iicia/a? ii?iae?ciaaiee ?ioaa?ae, aecia/aiee ca aeiiiiiaith oi?ioee Ia?naaaey. Ie iiaeaii oaia? ia?aienaoe oi?ioee (refif22), (refif23) aeey neiaie?a N_1,N_2 ianooiiei N_1(x,p)=H(x+fracihbar 2partial /partial p,p-fracihbar 2 partial /partial x)G(x,p), labelif27 N_2(x,p)=H(x-fracihbar 2partial /partial p,p+fracihbar 2 part?al /partial x)G(x,p). labelif28 O ne?i/aiiiaei??iiio aeiaaeeo oi?ioee eiiiiceoe?? iaaaaeai? o oaeiio a ?iaioax I.A.Ea?anueiaa oa A.I.Ianeiaa. O Ioieo? 2.2.3 ?icaeaa?oueny neiaieueia /eneaiiy iia?aoi??a c neiaieaie Oaa?aeaeaiiy 2.3. I?e Hin cal E iia?aoi? widehatH (aecia/aiee ca aeiiiiiaith oi?ioee Aeey fin bf D ie ia?ii: widehatHf=int W_fracx^prime 2U_hbar p^prime W_frac% x^prime 2fdxi _H(x^prime ,p^prime ). labelif18 Oaa?aeaeaiiy 2.4. Iaxae H,Gin cal E. Oiae?: widehatHwidehatG=widehatN% _1,;widehatGwidehatH=widehatN_2, aea N_1,N_2in cal E oa iathoue i?noea oi?ioee (refif22), (refif23) (c theta _Hequiv xi _H). sse iane?aeie ie io?eio?ii ocaaaeueiaiiy oi?ioee eiiooaoe?? (refif24) ia oeae aeiaaeie. O I?ae?icae?e? 2.3 ?icaeyaeathoueny IAeI c neiaieaie, ye? inoeeeththoue Oaa?aeaeaiiy 2.5. Iaxae G(x,p)=e^frac ihbar P(x,p), aea Pin cal P^2(cal H_-^2,bf R^1) P(x,p)= I?eionoeii, ui Cequiv det(I-K^2+K_1K_2)ne 0. Oiae? widehatG ? iaiaaeaiei o L_2(cal H_-,mu ) iia?aoi?ii, ii?ia yeiai Oaa?aeaeaiiy 2.6. Iaxae G caaeiaieueiy? oiiae iiia?aaeiuei? I?iiiceoe?? oa Hin cal E. ?icaeyiaii oaia? iia?aoi? widehatE_hbar c neiaieii E_hbar (x,p)=e^frac ihbar S(x,p),;Sin cal F_infty . labelif47 I/aaeaeii, ui E_hbar in cal F_infty, oae ui widehatE_hbar ? Oaa?aeaeaiiy 2.7. Iaxae left| Sright| _cal F aeinoaoiuei iaea. Oiae? a?aeia?aaeaiiy (0,1]ni hbar mapsto widehatE_hbar in cal L(L_2(cal H_-,mu )) labelif48 (aea cal L(H) iicia/a? i?ino?? e?i?eiex iaiaaeaiex iia?aoi??a a cal H) ? iaiaaeaiei. Ioieo 2.3.2 i?enay/aiee iiaoaeia? aneiioioe/iex ?ica’yce?a lbrack frac partial partial t-frac ihbar widehatH]T_t=O(hbar ), labelif62 T_0=?d, aea H=H_t oa i?eeia? ae?eni? cia/aiiy. Aoaeaii ooeaoe ?ica’ycie o inoeeeth/ei neiaieii U_t. Aiane?aeie oi?ioee eiiiiceoe?? oea ??aiyiiy aei ??aiyiiy a?aeiinii U_t: lbrack frac partial partial t-frac ihbar H(x+?frac partial partial p,p- ?frac partial partial x)]U_t(x,p)=O(hbar), U_0(x,p)=1. Iaoiae ?ica’ycaiiy ??aiyiue oaeiai oeio (yeee ? ocaaaeueiaiiyi Lambda _t o cal H_-^4, anioe?eiaaiee c aai?eueoii?aiii H(x+q,p-y), oa Oai?aia 2.4. ??aiyiiy (refif62) ia? ?ica’ycie T_t=T_t(H), yeee i?e aeinoaoiuei ia? aeaeyae T_t=hatU_t, aea U_t(x,p)=e^?S_t(x,p)/hbar f_t(x,p), labelif048 aea S_t ? ii?iaeaeoth/ith ooieoe??th iiiaiaeaeo Lambda _t, oa f_t ? Oai?aia 2.5. ??aiyiiy (refif62) ia? aeiaaeueiee ?ica’ycie T_tequiv T_t(H) ianooiiiai T_t=hatU_t_n-1,t_n…….hatU_t_1,t_2, labelig11 aea 0=t_1<...... aeinoaoiuei ae oa hatu_t_k-1 ia left t_k-1 aeaeo oeae caeaaeeoue ii modhbar a . o i iaei oeio iaoiae inaaaeiaeeoa ocaaaeueith eeane aea ioieo ie aecia oaeaeeiinoeeeethth aeniiiaioo. aeiaaaeaiith aneiioioe oi aeey oe nii aeiaiaeeii ianooiiee oai iaxae cal s aaiaxiaith aeaaa mu in m_infty s-cia aeaaeeex h v:cal hlongrightarrow neeueii aeeoa iaiaaeaiei iix oiae hbar longrightarrow aeeiio ianooiia int e z>mu (dz)+frac hbar 2int e^ Caeeoie ioe?ith?oueny o oiiieia?? cal S. Oeae ?acoeueoao oa eiai ocaaaeueiaiiy ia aeiaaeie i??e mu, yea Oai?aia 2.7. Iaxae S(x)=frac 12 bf R^1),;Bin cal L(H_-,cal H_+). Iaxae Hin cal D^2 (:=% cal P^2+cal F_infty , ae?eniicia/i?). Oiae?: beginarrayc e^-frac ihbar S(x)H(x,ihbar partial /partial x)e^frac ihbar S(x)phi (x)= =H(x,S^prime (x))phi (x)+ +hbar left[ ?Tr(fracpartial ^2Hpartial p^2(x,S^prime (x))S^prime prime (x))phi (x)+fracpartial Hpartial p% (x,S^prime (x))phi ^prime (x)right] + +O(hbar ^2), endarray aea caeeoie ioe?ith?oueny o ii?i? cal F(H_-,bf R^1). Iaoa ianooiia iaoa (bf Ioieo 2.4.3) – aeaoe eiino?oeoe?th aneiioioe/iex ?ica’yce?a caaea/? Eio? oeio beginarrayc left( frac partial partial t-frac ihbar H(x,ihbar partial /partial x)right) u(x,t)=Oleft( hbar ^2right) , u(x,0)=e^frac ihbar S_0(x)phi _0(x), endarray labelie1 aea S_0in cal D^2(cal H_-,bf R^1),;phi _0in cal F% _infty cal (H_-,bf R^1), i?eiaeii? i?e aeinoaoiuei iaeiio t. A?aeiia?aeii aei nxaie iaoiaeo AEA, ie aaiaeeii ??aiyiiy dotS_t(x)=H(x,S_t^prime (x)) labelie5 oa ??aiyiiy ia?aiino dotphi_t(x)=-Tr(fracpartial ^2Hpartial p^2(x,S_t^prime (x))S_t^prime prime (x))phi _t(x)+?fracpartial Hpartial p% (x,S_t^prime (x))phi _t^prime (x). labelie6 oa aeine?aeaeo?ii aeanoeaino? ?x ?ica’yce?a. I?ney oeueiai ie aeiaiaeeii Oai?aia 2.9. ?ica’ycie u_t caaea/? Eio? (refie1) ?nio? i?e t u_t(x)=e^frac ihbar S_t(x)phi _t(x), labelif119 aea S_t oa phi _t ? ?ica’yceaie a?aeiia?aeii ??aiyiue Aai?eueoiia-sseia? O I?ae?icae?e? 2.5 ie aeei?enoiao?ii io?eiai? ?acoeueoaoe aeey iiaoaeiae iiiaiaeae?a ? i?ino?? cal H^2, a a?aeia?aaeaiiy neeaeee ii?iaeaeothoueny aai?eueoii?aiai a?aeia?aaeaiue neeaeee. O Ioieo? 2.5.1 ie aecia/a?ii Iaxae cal K ? ae?eniei naia?aaaeueiei a?eueaa?oiaei i?inoi?ii, oa cal K_+subset cal Ksubset K_- eiai a?eueaa?oi-oi?aeo?anueea iniauaiiy. ?icaeyiaii i?ino?? Diff_cal psi :cal % Krightarrow K oaeex, ui psi (x)=x+Bx+l(x), aea B:cal K% _-rightarrow cal K_+ — aeayeee iaiaaeaiee e?i?eiee iia?aoi? oa aeaiaio lin cal F_infty (cal K_-,cal K_bf C). Ie aeiaiaeeii ianooiiee ?acoeueoao. Oaa?aeaeaiiy 2.9. Diff_cal F(cal K) ? i?aea?oiith a?oie aeeoaiii?o?ci?a Ie aecia/a?ii iiiaeeio Symp_cal F(cal H^2) ye neiieaeoe/io i?aea?oio Iicia/eii /a?ac ;gamma _H(t,tau ),;t,tau in [0,T]; ia?aoai?aiiy i?inoi?o Symp_cal F(cal H^2) ianooiiei /eiii. Oaa?aeaeaiiy 2.10. beginenumerate item Aeey aoaeue-yeex t,tau in [0,T];;;gamma _H(t,tau )in Symp_cal F(% cal H^2). item Aeey aoaeue-yeiai gamma in Symp_cal F(cal H^2) ?nio? aai?eueoii?ai endenumerate Iaxae oaia? gamma in Symp_cal F(cal H^2),;gamma =gamma _H(0,1) aeey aeayeiai H(t)in cal D^2. Cao?eno?ii i??o mu oa eioeeee alpha , ui T_gamma =T_t(H)_lceil t=1 labelipnl1 o i?inoi?? L_2(cal H_-,mu ), aea T_t(H) ? ?ica’yceii ??aiyiiy Oai?aia 2.10.A?aeia?aaeaiiy gamma longmapsto T_gamma labelipnl2 ? Ioieo 2.5.2 i?enay/aiee aecia/aiith oa aeine?aeaeaiith i?eionoeiex neiieaeoe/iex iiiaiaeae?a. Ie ?icaeyaea?ii iiiaiaeae cal M c iiaeaeeth cal K_- oa aoeanii cal U=(U_xi ,phi _xi)_xi in bf A , oa aea?ii ianooiia Aecia/aiiy 2.3-2.4. Aoean cal U iaceaa?oueny cal F -aoeanii, yeui eiai a?aeia?aaeaiiy neeaeee iaeaaeaoue Symp_cal F(cal H^2). O oeueiio aeiaaeeo cal E Aeae? ie ?icaeyaea?ii i?eeeaaee cal F- iiiaiaeae?a, ye? c’yaeythoueny ye Ioieo 2.5.3 i?enay/aiee iiaoaeia? ?iaa??aioiex IAeI c neiaieaie, Oai?aia 2.11. Aeey aeia?eueii? i??e mu oa eioeeeeo alpha ia cal H_-, ye? cal E(Xi ,bf C^1) a aeaaa?o e?i?eiex iia?aoi??a, ye? ae?thoue o frac ihbar [hatPhi,widehatG]=widehatPhi ,G+O(hbar ). ?acoeueoaoe ?icae?eo 2 iioae?eiaai? o ?iaioao [4, 5, 6, 7, 10, 11, 14]. O ?icae?e? 3 ie aea/a?ii eiie?aoiee i?eeeaae ?icaeyiooi? aeua widetildeH_mu o L_2(cal H_-,mu ) (yeee iaceaa?oueny iia?aoi?ii O I?ae?icae?e? 3.1 ie ?icaeyaea?ii eiino?oeoe?? I?ae?icae?e?a 2.2 oa 2.3 eiee mu ? aaonniaith i??ith, oa aoaeo?ii ?? iaaaeeeo iiaeeo?eaoe?th. Ie ?icaeyaea?ii aaonniao i??o eta c ei??aeyoe?eiei iia?aoi?ii hbar B^-1, aea B ? iaiaaeaiei aeiaeaoiei iai?ioiei neiao?e/iei iia?aoi?ii a cal H_eta ,V(x,p)=H_eta (x,p)+V(x) =-frac 12( +)+V(x). Iaxae g_V(t) ? cnoaii ocaeiaae ?ioaa?aeueiex e?eaex a?aeiia?aeii? nenoaie. Ie aeiaiaeeii, ui H_eta ,V,Gin cal E, g_V^*Gin cal E, gamma ^*H_eta ,V=H_eta ,V+h_eta ,V, aea h_eta ,V=h_eta ,V(gamma )in cal Oai?aia 3.2. Ia a?aeiia?aei?e iaeano? aecia/aiiy, ie ia?ii: 1) I?e Gin cal E frac ihbar [widetildeH_eta ,V,widehatG]=widehatH_eta ,V,G+O(hbar ^2). labelif65 2) I?e Gin cal D^2 (widetildeH_eta ,V+widehath_eta ,V)T_t(G)=T_t(G)widetilde% H_eta ,V+O(hbar ), labelif67 3) I?e Gin cal E widehat(g_V(t)^*G)exp(?twidetildeH_eta ,V)=exp(?twidetilde H_eta ,V)widehatG+O(hbar ^2), labelif66 aea exp(?twidetildeH_eta ,V) — iaeiiia?aiao?e/ia oi?oa?ia a?oia, ui O Ioieo? 3.2.3 ie ei?ioei iaaiai?th?ii aeiaaeie, eiee B ? iaiaiaaeaiei sse i?eeeaae aeei?enoaiiy ?icaeyiooi? aeua oai???, ie ?icaeyaea?ii ?aeyoea?nonueeiai aiciiiiai iiey. O Oai?ai? 3.3 ie i?aenoiiao?ii sse aoei iieacaii aeua, iiaoaeiaa aneiioioe/ieo ?ica’yce?a ??aiyiiue aeiaaa? ai?iiy ?ica’ycoaaoe eeane/i? ??aiyiy c neiaieaie Aeia?a a?aeiiei ? iaoiae aeine?aeaeaiiy aai?eueoiiiaeo nenoai ia aeoaeeaie Ioanniia, ui caiaeeoue iiaoaeiao ?ica’yce?a aei caaea/? Iaoae cal N ? aeaaeeei ae?eniei iiiaiaeaeii (??iaiiaei aai left f,gright (cal xi )= aea aai?eueoii?a iia?aoi? Psi :T^*cal Nlongrightarrow Tcal N acaaae? iae?i?eii caeaaeeoue a?ae cal xi in N. I?eionoeii, ui iiiaiaeae Psi = begintabularll Psi _+ & Psi _+- Psi _-+ & Psi _-% endtabular labeligeom2 aea Psi _+ oa Psi _- caeaaeaoue eeoa a?ae a?aeiia?aeieo cal %xi _+ oa xi Psi _0= begintabularlc Psi _+ & 0 multicolumn1c0 & multicolumn1l-Psi _- endtabular ?icaeyiaii oaciaee i?ino?? cal E iaae cal N. A?i ?iceeaaea?oueny ia A ieie? xi in cal N ioioiaeieii cal E=T^*G ?c %Gtimes cal N ca cal N_+ oa cal E__=G__times cal N__ (G=G_+times G__). Ie io?eio?ii ianooiiee ?acoeueoao. Oaa?aeaeaiiy 3.5. Iioaa?aeueia e?eaa nenoaie dotxi %=Psi _0dH,;Hin I(cal N), ?c ii/aoeii a aea xin G_+ oa yin G_- ? ?ica’yceii caaea/? oaeoi?ecaoe?? exp _xi _0tdH(xi _0)=x(t)stackrelxi _0*y(t). labelgeom7 O Ioieo? 3.3.2 ie ia?aiineii ia iane?i/aiiiaei??iee aeiaaeie a?oiiaee ia i?a?o? iane?i/aiiiaei??ii? a?oie E?, ? a?aeiia?aei? ?ioaa?aeuei? ?acoeueoaoe ?icae?eo 3 iioae?eiaai? o ?iaioao citeDP,D5,D6,D4,AD2. ?iaioa citeDP ? ni?eueiith c A.A.Iiaeeiec?iei. I?e oeueiio iinoaiiaea ?acoeueoao?a i?iaaaeai? ni?aaaoi?aie ni?eueii. AENIIAEE Aeena?oaoeiy i?enay/aia aeoaea iiioey?iie iaeanoi no/aniiai Oaeei /eiii, aea/aiiy eiaeiiai i?eeeaaeo aeiaaa? ?icaeoeo niaoeiaeueii? O aeenna?oaoe?? io?eiai? ianooii? iia? ?acoeueoaoe: 1) Iiaoaeiaaii eiiai?i?nii i?aaenoaaeaiiy i?aa?oi, ui ii?iaeaeaii 2) Aeiaaaeaii inioaaiiy oa ?aeeiinoue neeueieo ?ica’yce?a ianeii/aiiex 3) ?ic?iaeaii eiino?oeoeith IAeI c neiaieaie ia aieueaa?oiaiio oaciaiio i?inoi?i, ui aeithoue a L_2 ca aeaaeeith ii?ith ia aieueaa?oiaiio Aeiaaaeaii iniiaii aneiioioe/ii oi?ioee neiaieueiiai /eneaiiy oaeex iia?aoi?ia, cie?aia, oi?ioee eiiooaoe??, eiiiiceoe?? oa ae?? ia aeniiiaioo. Iiaoaeiaaii aneiioioe/ii ?ica’ycee aiaeiiaiaeiex oe?aeueiex ?iaiyiue O?aaeiiaa?a. 4) Iiaoaeiaaii aeaaa?o IAeI c neiaieaie ia i?eionoeiex neiieaeoe/iex iiiaiaeaeax, cie?aia, iiiaiaeaeax ?ica’yce?a iane?i/aiiiaei??ieo aaiieueoiiiaex nenoai. 5) Iia?aoi? Ae???xea aaonniai? ii?e ia aieueaa?oiaiio i?inoi?i ye aeaiaio aeaaa?e IAeI; aeiaaaeaii aiaeiiaiaeii aneiioioe/ii oi?ioee neiaieueiiai /eneaiiy. ?acoeueoaoe aeena?oaoei? ? iaeieie c ia?oex ?aaoey?iex ?acoeueoaoia o Iniiai? iieiaeaiiy aeena?oaoe?? iioae?eiaai? o ianooiieo ?iaioao: 1. Aeaeaoeeee A.TH., Iiaeeiecei A.A. A?oiiiaie iiaeoiae e 2. Daletskii A. Adler scheme analogue for non-linear Poisson brackets // 3. Aeaeaoeeee A.TH. Caaea/a oaeoi?ecaoeee a neiieaeoe/aneii a?oiiieaea e aaieeueoiiiau nenoaiu n iaeeiaeiuie neiaeaie Ioanniia // Aeiee. AI 4. Aeaeaoeeee A.TH. I eaiiie/aneii iia?aoi?a Ianeiaa ia eaa?aiaeaauo 5. Aeaeaoeeee A.TH. Aaneiia/iiia?iua o?aaiaiey O?aaeeiaa?a e 6. Daletskii A. Representations of canonical commutation relations 7. Daletskii A. Quasi-classical approximations for a one class of 8. Albeverio S., Daletskii A., Kondratiev Yu. A stochastic differential 9. Albeverio S., Daletskii A., Kondratiev Yu. A stochastic 10. Albeverio S., Daletskii A. Asymptotic quantization for solution 11. Daletskii A. Asymptotic expansions for a class of infinite 12. Albeverio S., Daletskii A., Kondratiev Yu. Infinite systems of 13. Albeverio S., Daletskii A., Kondratiev Yu. Some examples of 14. Albeverio S., Daletskii A. Algebras of pseudodifferential operators 15. Albeverio S., Daletskii A., Kondratiev Yu. Stochastic evolution on 16. Albeverio S., Daletskii A., Kondratiev Yu. Stochastic analysis on AIIOAOe?? Aeaeaoeueeee I.TH. Aeeoa?aioe?aeuei? oa inaaaeiaeeoa?aioe?aeuei? iane?i/aiiiaei??ieo iiiaiaeaeao. — ?oeiien. Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy aeieoi?a o?ceei-iaoaiaoe/ieo Aeena?oaoe?th i?enay/aii ?icaeoeo oai??? aeeoa?aioe?aeueieo oa ia iane?i/aiieo i?iaeaeo–iiiaiaeaeao oa aneiioioe/iei iaoiaeai inaaaeiaeeoa?aioe?aeueieo iia?aoi??a c neiaieaie ia a?eueaa?oiaiio Eeth/ia? neiaa: aeeoa?aioe?eiaia i??a, iia?aoi? Ae???oea, neiaieueia Aeaeaoeeee A.TH. Aeeooa?aioeeaeueiua e inaaaeiaeeooa?aioeeaeueiua aaneiia/iiia?iuo iiiaiia?aceyo. — ?oeiienue. Aeenna?oaoeey ia nieneaiea o/aiie noaiaie aeieoi?a oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.01 — iaoaiaoe/aneee aiaeec. – Einoeooo Aeenna?oaoeey iinayuaia ?acaeoeth oai?ee aeeooa?aioeeaeueiuo e inaaaaeiaeeooa?aioeeaeueiuo iia?aoi?ia n aeeueaa?oiaui oaciaui eaaceeeanne/aneea ?aoaiey niioaaonoaothueo o?aaiaiee O?aaeeiaa?a. iiiaiia?acee. Eeth/aaua neiaa: aeeooa?aioee?oaiay ia?a, iia?aoi? Aee?eoea, neiaieueiia Daletskii A.Yu. Differential and pseudodifferential operators on dimensional manifolds. — Manuscript. Thesis for a doctor degree by speciality 01.01.01- mathematical Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 1999. The thesis is devoted to the development of the theory of differential pseudodifferential operators with Hilbert (and Hilbert manifold) phase The introduction is devoted to the description of the field of In the first chapter Dirichlet operators associated with differentiable stochastic differential equations on the initial Riemannian manifold. An proved. The extremal Gibbs states are characterized in terms of The second chapter is devoted to the theory of infinite dimensional quickly oscillating exponent) are proved. Quasi-classical solutions of the aid of this representation the symbolic calculus for The third section is devoted to the study of a special case of the pseudodifferential operators. At the end, two geometric methods of Main results of the thesis have been published in 16 scientific Key words: differentiable measure, Dirichlet operator, Feller semigroup,
R
iai iio??ai?
/partial x) iiaea aooe aecia/aiee ca aeiiiiiaith oi?ioee:
/eiii:
aeaeyae?
a?eueo caaaeueiiai eeano cal E (yeee ii?iaeaeaiee neiaieaie, ui
?icaeyaeaeenue aeua, oa neiaieaie iie?iii?aeueiiai ?inoo). Oae? neiaiee
ii?iaeaeothoue, acaaae? eaaeo/e, iaiaiaaeai? IAeI. Eiaeia ooieoe?y H
eeano cal E ? ia?aoai?aiiyi Oo?’? ?iciiae?eo xi _H (yeee, acaaae?
eaaeo/e, ia ? i??ith). Ie aaiaeeii i?e?iaeio iaeanoue aecia/aiiy bf D oa
aeiaiaeeii ianooiia:
(refif12)) ? ei?aeoii-aecia/aiei ia iaeano? bf D oa caeeoa? ??
?iaa??aioiith.
i?e hbar to 0. O aeaeyae? oaeex iia?aoi??a io?eiothoueny ?ica’ycee
inaaaeiaeeoa?aioe?aeueiex ??aiyiue O?aae?iaa?a. O Ioieo? 2.3.1
aeiaiaeeoueny ei?aeoi?noue aecia/aiiy IAeI c inoeeethth/eie neiaieaie oa
aea/athoueny ?o aeanoeaino?.
(i?ino?? ae?eniex iaia?a?aiex iie?iii?a ae?oaiai ii?yaeeo ia cal
H_-^2),
aei??aith? C^-1. A?i caeeoa? ?iaa??aioiith iaeanoue bf D.
Oiae? aeey neiaiea N_1 eiiiiceoe?? widehatHwidehatG ia? i?noea oi?ioea
(refif27).
iaiaaeaiei iia?aoi?ii o L_2(cal H_-,mu ). Ianooiiee ?acoeueoao
eiio?ieth? eiai caeaaei?noue a?ae hbar .
inaaaeiaeeoa?aioe?aeueiex ??aiyiue O?aae?iaa?a. ?icaeyiaii ??aiyiiy
aeaeyae? IAeI c
caiaeeoueny
eeane/iiai AEA-iaoiaeo) ?icaeaa?oueny o I?ae?icae?e? 2.4. Ca?ac ie
aaiaeeii eaa?aiae?a iiiaiaeae
aeine?aeaeo?ii eiai aeanoeaino?. Ie aaiaeeii a?aeiia?aeia ??aiyiiy
ia?aiino oa aeiaiaeeii ianooii? ?acoeueoaoe.
iaeiio t
?ica’yceii a?aeiia?aeiiai ??aiyiiy ia?aiino.
aeaeyaeo:
caeaaeeoue a?ae hbar, aeei?enoiao?oueny o aeiaaaeaii? ianooiii?
oai?aie.
Aai?eueoiia-sseia?
ianooiiee ?acoeueoao.
aeinoaoiuei iaeiio ? ia? aeaeyae
oa ia?aiino.
aneiioioe/iiai eaaiooaaiiy eeano iane?i/aiiiaei??iex neiieaeoe/iex
iiiaiaeae?a (ye? ie iaceaa?ii cal F – iiiaiaeaeaie). Iiaeaeeth aeey oeex
aai?eueoii?aiaie eeano cal D^2. Ie aeei?enoiao?ii caaaeueio
eiino?oeoe?th aneiioioe/iiai eaaiooaaiiy: IAeI c neiaieaie ia cal F –
iiiaiaeae? aoaeothoueny ca aeiiiiiaith aneiioioe/iex ?ica’yce?a ??aiyiue
O?aae?iaa?a, ye? a?aeiia?aeathoue
a?oio i?eionoeiex eaiii?/iex ia?aoai?aiue a?eueaa?oiaiai oaciaiai
i?inoi?o oa aoaeo?ii ?? i?iaeoeaia i?aaenoaaeaiiy.
F(cal K) aeeoaiii?o?ci?a
i?inoi?o cal K.
a?oie Diff_cal F(cal H^2), oiaoi i?ino?? neiieaeoiii?o?ci?a gamma
i?inoi?o cal H^2 oaeex, ui gamma in Diff_cal F(cal H^2).
cal H^2, ii?iaeaeaia cnoaaie ocaeiaae ?ioaa?aeueiex e?eaex
aai?eueoiiiai? nenoaie, ui anioe?eiaaia c aai?eueoii?aiii H. Ie iiaeaii
ioa?aeoa?ecoaaoe i?ino??
H(t)in cal D^2 oaeee, ui gamma =gamma _H(0,1).
caaeiaieueiythoue oiiae I?ae?icae?eo 2.2, oa aaaaeaii iia?aoi?e
O?aae?iaa?a left( refif62right) .
i?iaeoeaiei aneiioioe/iei i?aaenoaaeaiiyi a?oie Symp_cal F(cal H^2).
neeaeee iaeaaeaoue Diff_cal F(cal K). Aeaa cal F – aoeane iaceaathoueny
aea?aaeaioieie, yeui ?x ia’?aeiaiiy ? cal F – aoeanii. Iiiaeeia an?x
aea?aaeaioiex cal F – aoean?a ia cal M iaceaa?oueny cal F-no?oeoo?ith.
Iiiaiaeae cal M c o?eniaaiith cal F -no?oeoo?ith iaceaa?oueny cal F –
iiiaiaeaeii. cal F-no?oeoo?a iiiaiaeaeo cal E iaceaa?oueny
neiieaeoe/iith cal F-no?oeoo?ith, yeui a?aeiia?aei? a?aeia?aaeaiiy
iaceaa?oueny neiieaeoe/iei cal F-iiiaiaeaeii.
iiiaiaeaee ?ica’yce?a iane?i/aiiiaei??iex aai?eueoiiiaex nenoai.
aecia/aieie ia neiieaeoe/iiio cal F-iiiaiaeae? Xi . Ie aeiaiaeeii
ianooiiee ?acoeueoao.
caaeiaieueiythoue oiiae I?ae?icae?eo 2.2, ?nio? aeiooie cal S(Xi )
e?i?eiex i?inoi??a iaae Xi (aecia/aiee mod;hbar ), oa a?aeia?aaeaiiy
Hlongmapsto widehatH ioanniiiai? aeaaa?e
i?inoi?? ia?aoei?a oeueiai aeiooea, oae?, ui ia? i?noea eiiooaoe?eia
oi?ioea
Caoaaaeeii, ui ?iaioe [4, 5, 6, 7, 11] ? naiino?eieie, a ?iaioe [10,
14]. — ni?eueieie c i?ioani?ii N.Aeueaaaa??i. I?e oeueiio iinoaiiaea
caaea/ oa iaaiai?aiiy ca’yce?a io?eiaieo ?acoeueoao?a c ?ioeie
iaeanoyie iaeaaeeoue iaii ni?aaaoi?ai. Aeiaaaeaiiy iniiaieo
?acoeueoao?a i?iaaaeai? aaoi?ii naiino?eii.
eiino?oeoe??. Ie ?icaeyaea?ii IAeI a L_2 ii aaonnia?e i???. O oeueiio
eiie?aoiiio aeiaaeeo ie aeine?aeaeo?ii ?x ca’ycie ?c iia?aoi?aie
Ae???xea. sseui ie ia?ii cal H_+- eaac??iaa??aioio i??o mu ia cal H_-,
ie iiaeaii ?icaeyiooe eeane/io oi?io Ae???xea cal E_mu , anioe?eiaaio c
oe??th i??ith, oa a?aeiia?aeiee aaia?aoi?
Ae???xea). Oeae iia?aoi? ia iiaea aooe aecia/aiee ca aeiiiiiaith
eiino?oeoe??, ?icaeyiooi? aeua. Iacaaaeath/e ia oea, ie iieaco?ii, ui
widetildeH_mu (i?eiaeii? o aeiaaeeo aaonniai? i??e mu ) iiaea aooe
aeeth/aiee a aeaaa?o IAeI.
o aeiaaeeo,
H, yeee caeeoa? ?iaa??aioiei i?ino?? cal H_+. O Oaa?aeaeaii? 3.1 ie
i?aenoiiao?ii ?acoeueoaoe iiia?aaei?x ?icae?e?a, aaeaioiaai? ia oeae
aeiaaeie. Aeae? ie ?icaeyaea?ii oaeiae aeiaaeie, eiee B ? iaiaiaaeaiei
(aeiaeaoiei neiao?e/iei) iia?aoi?ii. Ie aoaeo?ii a?aeiia?aeii iniauaiee
i?ino?? oa iaaiai?th?ii ocaaaeueiaiiy ?acoeueoao?a iiia?aaei?x ?icae?e?a
ia oeae aeiaaeie. O I?ae?icae?e? 3.2 ie ?icaeyaea?ii iia?aoi? Ae???xea
widetildeH_eta (Ioieo 3.2.1) oa eiai cao?aiiy widetildeH_eta ,V
(Ioieo 3.2.2) iaiaaeaiei cieco iioaioe?aeii Vin cal E(cal H_-,bf R^1).
Aa??noe/iee aai?eueoii?ai H_eta ,V, ui a?aeiia?aea? widetildeH_eta
,V, ia? ianooiiee aeaeyae:
aai?eueoiiiai?
E. Ianooiiee ?acoeueoao iieaco?, ui iia?aoi? widetildeH_eta ,V iiaea
aooe aeeth/aiee o aeaaa?o IAeI.
a?aeiia?aea? widetildeH_eta ,V.
neiao?e/iei aeiaeaoiei iia?aoi?ii a cal H, oa aeiaiaeeii aiaeia oai?aie
3.2.
aeiaaeie
?acoeueoaoe iiia?aaeiueiai ?icae?eo o oe?e neooaoe??. Oey oai?aia
iieaco?, ui iia?aoi? widetildeH_eta ,V_alpha ,varepsilon iiaea aooe
aeeth/aiee o aeaaa?o IAeI c neiaieaie eeano cal E((W_2^2-s(bf
R^n,q_s^-1))^2,bf C^1), aea W_2^2-s(bf R^n,q_s^-1) — i?ino?? Niaie?aa,
aecia/aiee ca aeiiiiiaith aeayei? aaaiai? iine?aeiaiino? q.
inaaaeiaeeoa?aioe?aeueieo
a?aeiia?aeieo IAeI o ?ie? ooieoe?e Aai?eueoiia. O I?ae?icae?e? 3.3 ie
iaaiaeeii aeae?eueea iaoiae?a aeine?aeaeaiiy oaeeo ??aiyiiue.
i?inoi?ao c e?i?eieie
oaeoi?ecaoe?? o a?aeiia?aei?e a?oi? E? (noaia Einoaioa-Aaeea?a), aai,
oi/i?oa, ?? aaiiao?e/iiai aa??aioo, ?ic?iaeaiiai ?aeiaiii oa
Naiaiiaei-Oyiue-Oaiuenueeei. O Ioieo? 3.3.1 ie i?iiiio?ii iiae?aiee
i?aeo?ae aeey aeiaaeeo iae?i?eieo aeoaeie. Iiaoaeiaa ?ioaa?aeueieo
e?eaeo caiaeeoueny aei caaea/? oaeoi?ecaoe?? a neiieaeoe/iiio a?oii?ae?
cal E, yeee a?ae?a?a? ?ieue oaciaiai i?inoi?o iaae ioanniiiaei
iiiaiaeaeii cal N. Oai??y oaeeo ia’?eo?a aoea ?ic?iaeaia Ea?anueiaei,
Ianeiaei oa Aaeiooaiii. O ?iaioao Ea?anueiaa oa Ianeiaa a?oiiaa
no?oeoo?a, a?aenooiy o aeiaaeeo iae?i?eieo aeoaeie Ioanniia,
cai?ith?oueny eieaeueiith no?oeoo?ith aeaaeeiai a?oii?aea cal E. A
ieie? cal xi in N i?ino?? cal E iiaea aooe i?aaenoaaeaiee ye ei-aeioe/ia
?icoa?oaaiiy T^*G c eaiii?/iith neieaeoe/iith no?oeoo?ith, aea G ?
ieieii ioey a bf R^n, ? ianooiieie no?oeoo?aie: aeiaooeii
xstackrelxi*y, ui caeaaeeoue a?ae xiin N, iia?aoi?ii ?iaa?n?? x_xi^-1,
xstackrelxi*x_xi^-1=e, oa ”aeniiiaioe?aeueiei a?aeia?aaeaiiyi”
exp_xi:T_xi^*cal Nrightarrow G.
a?eueaa?oiaei) c aeoaeeith Ioanniia
cal N iiaea aooe i?aaenoaaeaiee ye aeiaooie cal %N=N_+times cal N_-
aeaio ioanniiiaeo i?aeiiiaiaeae?a. Oiae? aai?eueoii?a iia?aoi? ia?
aei/io oi?io
__ a oi/oe? xi in cal N oa aecia/athoue aai?eueoiiia? iia?aoi?e Psi
_+:T^*cal N_+longrightarrow T% cal N_+ ? Psi _-:T^*cal N_-longrightarrow
Tcal N_-. Cai?iaaaeeii ia cal N iiao aeoaeeo Ioanniia left^.,^.right _0,
aecia/aio aai?eueoiiiaei iia?aoi?ii
aeiaooie cal E=E_+times cal E_- oaciaeo i?inoi??a iaae cal N%_+ oa cal
N_-. Neiieaeoe/ia no?oeoo?a ia cal E_pm ? caoaeaiiyi neiieaeoe/ii?
no?oeoo?e ia cal E. Oaciaee i?ino?? %cal E_0, ui a?aeiia?aea? aeoaeoe?
left cdot ,cdot right _0, oaeiae ia? oi?io cal E_0=cal E_+times cal E_-,
? neiieaeoe/ia oi?ia ia oeueiio i?inoi?? aei??aith? oi?iai ia
iiiaeieeao.
aeiiiiiaith a?aeia?aaeaiiy l. Oiae? cal E_+=G_+times
xi _0 ia? aeaeyae xi (t)=V_x(t)^-1(xi _0)equiv V_y(t)(xi _0) labelgeom6
iaoiae ?ioaa?oaaiiy iane?i/aiiiai eaioethaa Oiaee, yeee ocaaaeueith?
i?aeo?ae Ieueoaiaoeueeiai, Ia?aeiiiaa oa Aoaeiaia, Aaeeaoa. Eaioetha
Oiaee ?aae?co?oueny ye aai?eueoiiiaa nenoaia
e?ea? io?eiothoueny o oa?i?iao eii?e?aeiaii? ae?? ?? i?aea?oie (Oai?aia
3.4).
caaea/? oa ?ic?iaea iaoiaeo ?? ?ica’ycaiiy iaeaaeeoue aaoi?o.
Aeiaaaeaiiy aeayeeo aeiiii?aeieo
iaoaiaoe/iiai aiaeico — oai?i? aeeoa?aioe?aeueiex oa
inaaaeiaeeoa?aioe?aeueiex iia?aoi?ia ia ianeii/aiii-aeii?iex
iiiaiaeaeax. Oaei iia?aoi?e i?e?iaeii c’yaeythoueny o aaaaoueix iaeanoyx
iaoaiaoeee oa aiaeia?athoue aaaeeeao ?ieue o ?iciiiaiioiex caaea/ax
iaoaiaoe/ii? oa oai?aoe/ii? oiceee, oaeex ye noaoenoe/ia iaxaiiea oa
eaaioiaa oai?iy iiey. Ia aiaeiiio aiae aeiaaeeo ianeii/aiiiaeii?iex
eiiieiex oaciaex i?inoi?ia, ?icaeoie oei?? oai?i? ia iiiaiaeaeax
cono?i/a? aaaaoi ia?aoeiae, iia’ycaiex ic neeaaeiith aaiiao?i?th oaeex
iiiaiaeaeia oa aiaenooiinoth oaei? ?x oai?i?, yea ixiieth? ani aaaeeeai
i?eeeaaee.
oaxiiee.
iia?aoi?aie Ae???xea a?aan?anueeex ii? ia ianeii/aiiex aeiaooeax
eiiiaeoiex iiiaiaeaeia. Ca aeiiiiiaith oeeo i?aaenoaaeaiiue aeiaaaeaii
nooo?ao naiini?yaeaiiinoue oaeex iia?aoi?ia Ae???xea o ?aci
ianeii/aiiiai ?aiao aca?iiaeie oa io?eiaii iien aeno?aiaeueiex
a?aan?anueeex ii? ia ianeii/aiiex aeiaooeax eiiiaeoiex iiiaiaeaeia o
oa?iiiax a?aiaee/iinoi aiaeiiaiaeii? noixanoe/ii? aeeiaiiee.
nenoai noixanoe/iex aeeoa?aioe?aeueiex ?iaiyiue ia eiiiaeoiex
iiiaiaeaeax. Aeiaaaeaii eaaciiiaa?iaioiinoue ?iciiaeieia ?ica’yce?a
oaeex nenoai ia a?oiao E?.
i?inoi?i.
oaeaeeiinoeeethth/o
inaaaeiaeeoa?ai-
?aaeiciaaii
oeueiio iai?yieo. Iaea? oa iaoiaee, ui ?icaeiaii o aeena?oaoei?, aoee
aeei?enoaii o aaaaoueix iioex ?iaioax (aeea. iai?eeeaae, iineeaiiy
[8,97] aeena?oaoe??). Ana oea aeicaiey? c?iaeoe aeniiaie, ui
aeena?oaoeiy ? iiaei aaaeeeaei e?ieii o oai?i? ianeii/aiiiaeii?iex
aeeoa?aioe?aeueiex oa inaaaeiaeeoa?aioe?aeueiex iia?aoi?ia, a ??
?acoeueoaoe iathoue /eneaiii ca’ycee c aaaaoueia iioeie ?acoeueoaoaie o
oeie aaeoci i iiaeooue aooe aeei?enoaii o aaaaoueix aeineiaeaeaiiyx, ui
caeieniththoueny a Oe?a?ii oa ca ?? iaaeaie.
eioaa?e?iaaieth aaneiia/iie oeaii/ee Oiaeu // Oe?. iao. aeo?i. – 1988. –
40, N 4. – N. 445-447.
Non-linear and turbulent processes in physics, ed. V.G.Bar’yakhtar,
N.S.Erokhin, V.E.Zakharov, A.G.Sitenko, V.M.Chernousenko. – Kiev: Nauk.
Dumka, 1988. – C. 48-51.
NNN?. – 1989. – 40, N 2. – N. 389-393.
iiiaiia?aceyo n aeeueaa?oiaie iiaeaeueth // Iao. caiaoee. – 1990. – 48,
N 6. – N. – 51-60.
i?aaenoaaeaiea a?oiiu neiieaeoe/aneeo i?aia?aciaaiee aeeueaa?oiaa
oaciaiai i?ino?ainoaa // Ooieoeeii. aiaeec e aai i?ee. – 1992. – 26, N
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infinite
analysis.
and pseudodifferential operators on infinite dimensional manifolds. Such
operators appear in different parts of mathematics and mathematical
physics. The main attention is paid to the probabilistic approach of
study of second order elliptic operators on product-manifolds (infinite
products of compact Riemannian manifolds) and to asymptotic methods of
investigation of
spaces. The thesis consists of introduction, 3 chapters and references.
investigations, a review of existing results in this field and
description of the main results of the thesis.
measures on product-manifolds are considered. The stochastic dynamics
generated by these operators is constructed via stochastic differential
equations approach. That is, the Dirichlet operator is realized as a
generator of a Markov process given as the solution to an infinite
system of
existence and uniqueness theorem for such systems is proved and
properties of solutions are studied. In particular, quasi-invariance of
distributions of the solutions (in the case where the initial manifold
has a Lie group structure) is proved. These results are applied to the
investigation of Glauber dynamics of some lattice models of statistical
mechanics. In particular, the existence of Feller semigroups associated
with Gibbs measures on product-manifolds is proved and their explicit
construction is given. The essential self-adjointness of the generator
on the space of cylinder functions (even in the case of interactions of
infinite range) is
ergodicity of the dynamics. Dirichlet forms on loop and diffeomorphism
groups are defined and their closability is proved.
pseudodifferential operators. An algebra of such operators with symbols
on Hilbert phase spaces is constructed. These operators are constructed
as functions of elementary operators of multiplication and
differentiation symmetrized w.r.t. a smooth measure on Hilbert space.
The main asymptotic formulae of the symbolic calculus (formulae for
symbols of composition commutator of two pseudodifferential operator,
formula of action on a
the corresponding pseudodifferential Schr”odinger equations in the form
of pseudodifferential operators with oscillatory symbols are obtained.
For this, the infinite dimensional version of WKB method was developed.
These solutions gave the possibility to construct an asymptotic
projective representation of the group of symplectomorphisms of the
phase space. With
pseudodifferential operators with symbols on certain infinite
dimensional symplectic manifolds is constructed. As an example, spaces
of solutions to infinite dimensional Hamiltonian systems are considered
and their asymptotic quantization is constructed.
construction above. Namely, pseudodifferential operators in the space of
square integrable functions w.r.t. a Gaussian measure on a Hilbert space
are considered. In this special case, the corresponding Dirichlet
operator and its potential perturbations are considered as elements of
the algebra of
integration of infinite dimensional classical Hamiltonian equations are
proposed (which is required by the quasi-classical approach to the
investigation pseudodifferential equations). In particular, integral
curves of Hamiltonian equations associated with certain non-linear
Poisson brackets are obtained as solutions of a factorization problem in
a symplectic groupoid.
publications and reported at a number of international scientific
conferences.
pseudodifferential operator, symbolic calculus, phase space, infinite
dimensional manifold.
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