Euea?anueeee aea?aeaaiee oi?aa?neoao

?iai? ?aaia O?aiea

Aeieo?eoei Ia?’yi ?aaiiae/

OAeE 517.98

AAEOI?E AENIIIAIOe?AEUeIIAI OEIO

IIA?AOI??A ?C AeENE?AOIEI NIAEO?II

IAAe AAIAOIAEIE I?INOI?AIE

— iaoaiaoe/iee aiae?c

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

EUeA?A — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a ?inoeooo? i?eeeaaeieo i?iaeai iaoai?ee ? iaoaiaoeee
?i. ss.N. I?aeno?eaa/a Iaoe?iiaeueii? Aeaaeai?? iaoe Oe?a?ie.

Iaoeiaee ea??aiee aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Eiiooainueeee Ieaa Aaneeueiae/,

?inoeooo i?eeeaaeieo i?iaeai iaoai?ee ?

iaoaiaoeee ?i. ss.N. I?aeno?eaa/a IAI Oe?a?ie,

caa?aeoaa/ a?aeae?eo ooieoe?iiaeueiiai aiae?co.

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

?aaeeii sse?a Aaeaioeiiae/,

A?ei?onueeee aea?aeaaiee oi?aa?neoao,

caa?aeoaa/ eaoaae?ith ooieoe?iiaeueiiai aiae?co;

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

*a?aiieo ?aaai Aaneeueiae/,

Aea?aeaaiee oi?aa?neoao “Euea?anueea iie?oaoi?ea”,

aeioeaio eaoaae?e aeui? iaoaiaoeee.

I?ia?aeia onoaiiaa ?inoeooo iaoaiaoeee IAI Oe?a?ie,

a?aeae?e aeeoa?aioe?aeueieo ??aiyiue c /anoeiieie iio?aeieie, i. Ee?a.

Caoeno a?aeaoaeaoueny 20 o?aaiy 1999 ?ieo i 15.20 ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.051.07 o Euea?anueeiio aea?aeaaiiio
oi?aa?neoao? ?iai? ?aaia O?aiea ca aae?anith:

290602, i. Euea?a, aoe. Oi?aa?neoaonueea,1 (aoaeeoi??y 377).

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? Euea?anueeiai
aea?aeaaiiai oi?aa?neoaoo ?iai? ?aaia O?aiea (aoe. Ae?aaiiaiiaa, 5).

Aaoi?aoa?ao ?ic?neaiee 19 ea?oiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Ieeeothe ss.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aiae?oe/i? aaeoi?e a eiioaeno? i?aaenoaaeaiue a?oi
aoei aaaaeaii a ?iaioao Oa?eo-*aiae?e (1953). A oai??th e?i?eieo
iaiaiaaeaieo iia?aoi??a iiiyooy oaeiai aaeoi?a cai?iaaaeea Iaeuenii o
ca’yceo ?c i?iaeaiith ?nioaaiiy naiini?yaeaieo ?icoe?aiue iia?aoi??a.
TH.I. Aa?acainueeei anoaiiaeaii e?eoa??e naiini?yaeaiino? iia?aoi??a o
oa?i?iao a?eueo caaaeueiiai iiiyooy — eaac?aiae?oe/iiai aaeoi?a.

A eean? aiae?oe/ieo aaeoi??a aeae?eythoue oe?e? aaeoi?e
aeniiiaioe?aeueiiai oeio. Eieaeueii iioee? oa ii?iiaai? i?inoi?e
aaeoi??a aeniiiaioe?aeueiiai oeio iaiaiaaeaieo iia?aoi??a iaae
aaiaoiaeie i?inoi?aie aeine?aeaeoaaeenue a ?iaioao ss.A. ?aaeeii
(1985). Iei, cie?aia, iiaoaeiaaii iia?aoi?ia /eneaiiy, a oaeiae
anoaiiaeaia u?euei?noue iiiaeeie oaeeo aaeoi??a aeey aaia?aoi??a
iaiaaeaieo neeueii iaia?a?aieo a?oi.

I.E. Ai?aa/oeii ? A.?. Ai?aa/oe (1995) anoaiiaeaii u?euei?noue
aaeoi??a aeniiiaioe?aeueiiai oeio aeey iia?aoi??a ?c a?aeie?aiethaaiei
niaeo?ii, aaaaeaiiai TH.?. Ethae/ai ? A.?. Iaoea?aei (1960), o
i?eiouaii? ui ?o ?acieueaaioa caaeiaieueiy? oiia? Eaa?iniia ? niaeo?
eaaeeoue ia ae?eni?e in?.

A.A. ?aaec??anueeei (1997) ?ica’ycaia i?iaeaia iaee?aueo iaaeeaeaiue
aeaiaio?a aaiaoiaiai i?inoi?o aaeoi?aie aeniiiaioe?aeueiiai oeio
iaiaiaaeaieo iia?aoi??a. Anoaiiaeaii ioe?iee caa?oo oaeeo iaaeeaeaiue
/a?ac K- ooieoe?iiaee (ia??aiino? oeio Aeaeaeniia), a oaeiae ioe?iee
caa?oo K- ooieoe?iiae?a /a?ac oae? iaaeeaeaiiy (ia??aiino? oeio
Aa?iooaeia). Ca?aene, ye /anoeiiee aeiaaeie, aeieeaa? ?yae eeane/ieo
oai?ai c oai??? iaaeeaeaiue ooieoe?e o?eaiiiiao?e/ieie iie?iiiaie oa
oe?eeie ooieoe?yie aeniiiaioe?aeueiiai oeio.

Oaeei /eiii, eiei i?iaeai, aea aeei?enoiao?oueny oaoi?ea aaeoi??a
aeniiiaioe?aeueiiai oeio, ioiieth? cia/io /anoeio niaeo?aeueii? oai???
iia?aoi??a iaae aaiaoiaeie i?inoi?aie oa ?? canoinoaaiue. Oea
i?aeoaa?aeaeo? aeooaeuei?noue oaie aeena?oaoe?eii? ?iaioe.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?y
aeeiioaaeanue o ?aieao iaoeiai-aeine?aeii? oaie «?ic?iaea iia?aoi?ieo oa
aaiiao?e/ieo iaoiae?a ooieoe?iiaeueiiai aiae?co ia iniia? oai???
oiiieia?/ieo aeaaa? ? ?o canoinoaaiiy aei aeine?aeaeaiiy iae?i?eieo
aaiethoe?eieo ??aiyiue o aaiaoiaeo i?inoi?ao» (iiia? aea?aeaaii?
?a?no?aoe?? 0193U033339) a?aeae?eo ooieoe?iiaeueiiai aiae?co ?inoeoooo
i?eeeaaeieo i?iaeai iaoai?ee ? iaoaiaoeee ?i. ss.N. I?aeno?eaa/a IAI
Oe?a?ie.

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith aeena?oaoe?? ? iien aaeoi??a
aeniiiaioe?aeueiiai oeio iia?aoi??a ?c aeene?aoiei niaeo?ii iaae
aaiaoiaeie i?inoi?aie, iiaoaeiaa aeey oaeeo iia?aoi??a
ooieoe?iiaeueiiai /eneaiiy a ?ioa?iieyoe?eieo eeanao neiaie?a, a oaeiae
canoinoaaiiy iaea?aeaieo ?acoeueoao?a aei oai??? aeeoa?aioe?aeueieo
iia?aoi??a o ooieoe?iiaeueieo i?inoi?ao.

O aeena?oaoe??, cie?aia, ?icaeyiooi

— i?iaeaio oa?aeoa?ecaoe?? ne?i/aiieo i?yieo noi ei?aiaaeo
i?aei?inoi??a ca aeiiiiiaith aaeoi??a aeniiiaioe?aeueiiai oeio o
aeiaaeeo aano?aeoieo iia?aoi??a,

— ooieoe?iiaeuei? i?inoi?e ei?aiaaeo ooieoe?e ?aaoey?ieo ? aeayeeo
neeueii ae?iaeaeaieo ae?ioe/ieo a?aie/ieo caaea/,

— i?iaeaio iieno eeano neiaie?a ooieoe?iiaeueiiai /eneaiiy iia?aoi??a
?c aeene?aoiei niaeo?ii o eeanao caieiaieo iia?aoi??a.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. O aeena?oaoe?? aeey
iia?aoi??a ?c aeene?aoiei niaeo?ii iaae aaiaoiaeie i?inoi?aie

— ciaeaeaii iien ne?i/aiieo i?yieo noi ei?aiaaeo i?aei?inoi??a
iia?aoi??a o oa?i?iao ?o aaeoi??a aeniiiaioe?aeueiiai oeio,

?aaoey?ieo ae?ioe/ieo iia?aoi??a iaae iaiaaeaieie iaeanoyie
aaee?aeiaiai i?inoi?o ? ia eiiiaeoieo iiiaiaeaeao, a oaeiae aeayeeo
neeueii ae?iaeaeaieo ae?ioe/ieo iia?aoi??a ? ocaaaeueiaieo iia?aoi??a
Eaaeaiae?a,

— iiaoaeiaaii ooieoe?iiaeueia /eneaiiy a ?ioa?iieyoe?eieo aeaaa?ao
neiaie?a aeey caieiaieo iia?aoi??a, cie?aia, anoaiiaeaii aeaaa?a?/iee
?ciii?o?ci aeaaa?e neiaie?a a?eiiooaioia? caaeaiiai iia?aoi?a iaae
ei?aiaaeie aaeoi?aie, iieacaii ?nioaaiiy caieeaiiy ooieoe?e a?ae
iia?aoi?a ? aeine?aeaeaii aeanoeaino? a?aeia?aaeaiiy niaeo?o.

Iacaai? ?acoeueoaoe ? iiaeie. Aiie ?icaeaathoue ?acoeueoaoe
aeine?aeaeaiue ?yaeo aaoi??a, cie?aia, I.E. Ai?aa/oea, A.A.
?aaec??anueeiai, ss.A. ?aaeeii — o aeiaaeeo aano?aeoieo iia?aoi??a,
N. Aaiiia, E. I??aiaa?aa, O. O??aaey — o aeiaaeeo ae?ioe/ieo
aeeoa?aioe?aeueieo iia?aoi??a.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?acoeueoaoe aeena?oaoe??
iathoue oai?aoe/ia cia/aiiy. Aiie ciaoiaeyoue canoinoaaiiy a oai???
aeeoa?aioe?aeueieo ??aiyiue ?c /anoeiieie iio?aeieie ? iaoaiaoe/i?e
o?ceoe?.

Iniaenoee aianie caeiaoaa/a. Iaaaaeai? a aeena?oaoe?? iniiai?
?acoeueoaoe io?eiai? aaoi?ii naiino?eii. Iaoeiaiio ea??aieeo iaeaaeeoue
iinoaiiaea caaea/ ? caaaeueia ea??aieoeoai ?iaioith.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe aeena?oaoe??
aeiiia?aeaeenue ia: V-e I?aeia?iaei?e iaoeia?e eiioa?aioe?? ?i. aeaae.
I. E?aa/oea (i. Ee?a, 1996?.); Anaoe?a?inuee?e eiioa?aioe??
«Aeeoa?aioe?aeueii-ooieoe?iiaeuei? ??aiyiiy oa ?o canoinoaaiiy» (i.
*a?i?aoe?, 1996?.); I?aeia?iaei?e eiioa?aioe?? «Oai??y ai?ieneiaoe?e oa
/enaeuei? iaoiaee» (i. ??aia, 1996?.); Anaoe?a?inuee?e iaoeia?e
eiioa?aioe?? «Iia? i?aeoiaee aei ?ica’ycaiiy aeeoa?aioe?aeueieo
??aiyiue» (i. Ae?iaiae/, 1997?.); VII-e I?aeia?iaei?e iaoeia?e
eiioa?aioe?? ?i. aeaae. I. E?aa/oea (i. Ee?a, 1998?.); I?aeia?iaei?e
eiioa?aioe?? «No/ani? i?iaeaie iaoai?ee ? iaoaiaoeee» (i. Euea?a,
1998?.); I?aeia?iaei?e iaoeia?e eiioa?aioe?? «No/ani? i?iaeaie
iaoaiaoeee» (i.*a?i?aoe?, 1998?.); nai?ia?ao ?c ooieoe?iiaeueiiai
aiae?co Euea?anueeiai aea?aeaaiiai oi?aa?neoaoo ?i. ?. O?aiea oa ?IIII
?i. ss.N. I?aeno?eaa/a IAI Oe?a?ie; ?aa?iiaeueiiio nai?ia?? c
iaoaiaoe/iiai aiae?co.

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a
iaeeiaaeoeyoe ?iaioao, c yeeo i’youe o aeaeaiiyo, caoaa?aeaeaieo AAE
Oe?a?ie, oa o?noue o iaoa??aeao I?aeia?iaeieo ? Anaoe?a?inueeeo iaoeiaeo
iaoaiaoe/ieo eiioa?aioe?e.

No?oeoo?a ? ia’?i ?iaioe. Aeena?oaoe?y neeaaea?oueny ?c anooio, o?ueio
?icae?e?a, ?icaeoeo ia i?ae?icae?ee, aeniiae?a ? nieneo aeei?enoaieo
aeaea?ae. Ianya aeena?oaoe?? 126 noi?. Nienie aeei?enoaieo aeaea?ae
aeeth/a? 90 iaeiaioaaiue.

CI?NO ?IAIOE

O anooi? aeaii caaaeueio oa?aeoa?enoeeo ?iaioe. Cie?aia, iaa?oioiaaii
aeooaeuei?noue oaie, i?aeoe/ia cia/aiiy iaea?aeaieo a aeena?oaoe??
?acoeueoao?a.

O ia?oiio ?icae?e? iiaeaii iaeyae i?aoeue, ye? noinothoueny oaiaoeee
?iaioe. Iaaaaeaii iniiai? iiiyooy oa oai?aie, ui aeei?enoiaothoueny o
aeena?oaoe??. Noi?ioeueiaaii iniiai? ?acoeueoaoe, ye? aeiinyoueny ia
caoeno.

O ae?oaiio ?icae?e? aeine?aeaeothoueny aaiaoia? i?inoi?e aaeoi??a
aeniiiaioe?aeueiiai oeio, ?ciii?oi? ne?i/aiiei i?yiei noiai ei?aiaaeo
i?aei?inoi??a iia?aoi??a ?c aeene?aoiei niaeo?ii, ui ae?thoue iaae
aaiaoiaeie i?inoi?aie. Ca ?o aeiiiiiaith iienaii i?inoi?e, yeei
iaeaaeaoue ei?aiaa? ooieoe?? ?yaeo ?aaoey?ieo ? ae?iaeaeaieo ae?ioe/ieo
iia?aoi??a ?c aeene?aoiei niaeo?ii, a oaeiae aeeoa?aioe?aeueieo
iia?aoi??a Eaaeaiae?a.

.

aecia/eii i?ino?? aeaeyaeo

.

aea c — iacaeaaeia a?ae k iino?eia.

.

.

iaceaa?oueny iia?aoi?ii ?c aeene?aoiei niaeo?ii, yeui:

c ?aeeiith oi/eith neoi/aiiy ia aaciaaeiino?;

? eiio a?aeiia?aea? ne?i/aiiiaei??iee ei?aiaaee i?aei?ino??

,

.

, iia’ycai? ianooiiei /eiii.

Eaia 2.1.4. Aeey aeia?eueiiai iia?aoi?a A ?c aeene?aoiei niaeo?ii
ni?aaaeaeo?oueny ??ai?noue

.

Ianooiia oai?aia ? iniiaiei ?acoeueoaoii ae?oaiai ?icae?eo. Aiia iieno?
ne?i/aii? i?yi? noie ei?aiaaeo i?aei?inoi??a iia?aoi?a c aeene?aoiei
niaeo?ii a oa?i?iao eiai aaeoi??a aeniiiaioe?aeueiiai oeio.

ni?aaaeaeo?oueny ??ai?noue

.

ne?i/aiiiaei??i?.

— oe?eeo ooieoe?e aeniiiaioe?aeueiiai oeio n eiiieaenieo ci?iieo.

O i?ae?icae?e? 2.3 iienaii i?inoi?e ei?aiaaeo ooieoe?e ?aaoey?ieo
ae?ioe/ieo aeeoa?aioe?aeueieo iia?aoi??a a iaiaaeaieo iaeanoyo .

? iaa?? iia?aoi??a

, (2.13)

,

?aaoey?ii ae?ioe/iee.

?icaeyiaii caieiaiee iia?aoi? A, caaeaiee ni?aa?aeiioaiiyie

, (2.14)

.

Oai?aia 2.3.1. Iaoae A- iia?aoi?, caaeaiee ni?aa?aeiioaiiyie (2.14).
Oiae? ni?aaaaeeea? ??aiino?

.

Ianooiia oai?aia iieno? i?ino?? ei?aiaaeo ooieoe?e iia?aoi?a,
ii?iaeaeaiiai ?aaoey?iith ae?ioe/iith caaea/ath, o aeiaaeeo iino?eieo
eiao?oe??io?a ??aiyiiy.

iia?aoi?a A ? iino?eieie, oi

.

Oai?aia 2.3.2 o i?ae?icae?e? 2.4 ocaaaeueith?oueny ia aeiaaeie
aeeoa?aioe?aeueieo iia?aoi??a ia iiiaiaeaeao.

iiaeia cia?aceoe o aeaeyae?

, (2.25)

oaea, ui

.

ia? iaii?iaeith ?acieueaaioio iiiaeeio. Oiae? ni?aaaaeeea? ??aiino?

,

.

) i?eioneathoue ?icoe?aiiy aei oe?eeo ooieoe?e aeniiiaioe?aeueiiai
oeio (n-1) eiiieaenieo ci?iieo.

O i?ae?icae?e? 2.5 ca aeiiiiiaith aaeoi??a aeniiiaioe?aeueiiai oeio
iienaii oaeiae i?inoi?e ei?aiaaeo ooieoe?e ?yaeo neeueii ae?iaeaeaieo
ae?ioe/ieo iia?aoi??a.

ni?aaaaeeea? ??aiino?

,

.

O i?ae?icae?e? 2.6 aeine?aeaeothoueny ocaaaeueiai? aeeoa?aioe?aeuei?
iia?aoi?e Eaaeaiae?a.

.

?c icia/aiiy 2.6.1.

O o?aoueiio ?icae?e? iiaoaeiaaii ooieoe?iiaeueia /eneaiiy a
?ioa?iieyoe?eieo eeanao neiaie?a aeey iia?aoi??a ?c aeene?aoiei niaeo?ii
oa u?eueiei i?inoi?ii aaeoi??a aeniiiaioe?aeueiiai oeio.

Aeae? A — iia?aoi? ?c aeene?aoiei niaeo?ii iaae aaiaoiaei i?inoi?ii (
oa u?eueiei ca ii?iith i?aei?inoi?ii aaeoi??a aeniiiaioe?aeueiiai oeio.

-aei??iee eiiieaeniee aaeoi?iee i?ino??

c ii?iith

,

.

? eiiooaoeaiith aaiaoiaith aeaaa?ith a?aeiinii cai?oee

,

aea

,

.

iinoaaeii o a?aeiia?aei?noue i?yiee aeiaooie aeaaa?

oa iieii?aeeiaoiei iiiaeaiiyi aeaiaio?a

,

aeaeyaeo

, ye? caaeiaieueiythoue ni?aa?aeiioaiiy

,

, iaae?eaiei aeene?aoiith oiiieia??th, ? a?aeiia?aeia ia?aoai?aiiy
Aaeueoaiaea

ia ce?/aiiee i?yiee aeiaooie iiey C ?c iieii?aeeiaoiei iiiaeaiiyi
aeaiaio?a.

.

.

ooieoe?iiaeueiiai /eneaiiy aeey iia?aoi?a A iaae i?inoi?ii eiai
ei?aiaaeo aaeoi??a.

Oai?aia 3.2.1. (a) A?aeia?aaeaiiy

.

(b) A?aeia?aaeaiiy

,

.

.

.

.

? ?? a?aeiia?aeieo iio?aeieo o oi/eao niaeo?a).

Oai?aia 3.2.1 aeicaiey? ?icaeiooe aeey iia?aoi?a A ooieoe?iiaeueia
/eneaiiy a eean? caieiaieo iia?aoi??a iaae B.

iaae B ?c iaeanoth aecia/aiiy

Ia iniia? oai?aie 3.3.1, ye ? a eeane/iiio aeiaaeeo, iiaeia aeiaanoe
aiaeia oai?aie i?i neeaaei? ooieoe??.

Oai?aia 3.4.2. I?eionoeii, ui aeeiiothoueny ianooii? oiiae:

.

ni?aaaaeeeaa ni?aa?aeiioaiiy

.

AENIIAEE

O ?iaio? aeey iia?aoi??a ?c aeene?aoiei niaeo?ii iaae aaiaoiaeie
i?inoi?aie iienaii i?inoi?e aaeoi??a aeniiiaioe?aeueiiai oeio, ui
ni?aiaaeathoue c i?yieie noiaie ei?aiaaeo i?aei?inoi??a, ? anoaiiaeaii,
ui i?ino?? an?o aaeoi??a aeniiiaioe?aeueiiai oeio ca?aa?oueny c
i?inoi?ii ei?aiaaeo aaeoi??a.

A oa?i?iao aaeoi??a aeniiiaioe?aeueiiai oeio iaaaaeaii iien i?inoi?o
ei?aiaaeo ooieoe?e ?aaoey?ieo ? aeayeeo neeueii ae?iaeaeaieo ae?ioe/ieo
iia?aoi??a, a oaeiae ocaaaeueiaieo aeeoa?aioe?aeueieo iia?aoi??a
Eaaeaiae?a.

Iiaoaeoaaii ooieoe?iiaeueia /eneaiiy a ?ioa?iieyoe?eieo eeanao neiaie?a
aeey iia?aoi??a ?c aeene?aoiei niaeo?ii oa u?eueiei i?aei?inoi?ii
aaeoi??a aeniiiaioe?aeueiiai oeio. Anoaiiaeaii aiaeiae oai?ai i?i
a?aeia?aaeaiiy niaeo?o ? neeaaei? ooieoe?? a?ae oaeeo iia?aoi??a.

Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a ?iaioao:

1. Aeieo?eoei I.?., Eiiooainueeee I.A. Aaceni?noue nenoai ei?aiaaeo
aaeoi??a iia?aoi??a c eiiiaeoiith ?acieueaaioith // Aeii. IAI Oe?a?ie.
1997. — ? 9. — N.28-32.

2. Aeieo?eoei I.?. Aeaye? aeanoeaino? ei?aiaaeo aaeoi??a iia?aoi??a c
aeene?aoiei niaeo?ii // Iao. iaoiaee ? o?c.-iao. iiey. — 1997. — O.40,
? 2. — N.36-38.

3. Dmytryshyn M.I., Lopushansky O.V. Vectors of exponential type of
operators with discrete spectrum // Iaoaiaoe/i? nooae??. I?aoe?
Euea?anueeiai iaoai. o-aa. — 1998. — O.9, ? 1.- N.70-77.

4. Aeieo?eoei I.?., Eiiooainueeee I.A. Ooieoe?iiaeueia /eneaiiy iiaieo
iia?aoi??a c aeene?aoiei niaeo?ii // Iao. iaoiaee ? o?c.-iao. iiey. —
1998. — O.41, ? 1. — N.127-135.

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aaeoi??a iia?aoi?a c eiiiaeoiith ?acieueaaioith // Oace aeiiia?aeae
V-i? I?aeia?. iaoeiai? eiio. ?i. aeaae. I. E?aa/oea. — Ee?a. — 1996. —
N.126.

6. Aeieo?eoei I.?., Eiiooainueeee I.A. I?i aaceni?noue ei?aiaaeo
i?aei?inoi??a iia?aoi?a c eiiiaeoiith ?acieueaaioith // Oace aeiiia?aeae
Anaoe?a?inueei? eiio. «Aeeoa?aioe?aeueii-ooieoe?iiaeuei? ??aiyiiy oa ?o
canoinoaaiiy». — Ee?a. — 1996. — N.51.

7. Aeieo?eoei I.?. Aaceni?noue ei?aiaaeo i?aei?inoi??a iia?aoi?a c
eiiiaeoiith ?acieueaaioith // Oace aeiiia?aeae I?aeia?. eiio. «Oai??y
ai?ieneiaoe?e oa /enaeuei? iaoiaee». — ??aia. — 1996. — N.28.

8. Aeieo?eoei I.?., ?yaenueea A.A. I?i i?ino?? aaeoi??a
aeniiiaioe?aeueiiai oeio iia?aoi?a ocaaaeueiaiiai aeeoa?aioe?thaaiiy //
Oace aeiiia?aeae Anaoe?a?inueei? iaoeiai? eiio. «Iia? i?aeoiaee aei
?ica’ycaiiy aeeoa?aioe?aeueieo ??aiyiue». — Ee?a. — 1997. — N.41.
(Caeiaoaa/o iaeaaeeoue oai?aia 1).

9. Aeieo?eoei I.?. Ooieoe?iiaeueia /eneaiiy aeey iia?aoi??a c
aeene?aoiei niaeo?ii // Iaoa??aee VII-i? I?aeia?. iaoeiai? eiio. ?i.
aeaae. I. E?aa/oea. — Ee?a. — 1998. — N.148.

10. Aeieo?eoei I.?. Aiae?oe/i?noue ei?aiaaeo ooieoe?e ?aaoey?ii?
ae?ioe/ii? a?aie/ii? caaea/? // Iaoa??aee I?aeia?. iaoeiai? eiio.
«No/ani? i?iaeaie iaoai?ee ? iaoaiaoeee». — Euea?a. — 1998. — N.270.

11. Aeieo?eoei I.?. Ooieoe?iiaeueia /eneaiiy ia ei?aiaaeo aaeoi?ao
iia?aoi?a c aeene?aoiei niaeo?ii // Iaoa??aee I?aeia?. iaoeiai? eiio.
«No/ani? i?iaeaie iaoaiaoeee». — *anoeia 1. — Ee?a: ?i-o iaoaiaoeee IAI
Oe?a?ie. — 1998. — N.178-179.

AIIOAOe??

Aeieo?eoei I ?. Aaeoi?e aeniiiaioe?aeueiiai oeio iia?aoi??a ?c
aeene?aoiei niaeo?ii iaae aaiaoiaeie i?inoi?aie. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.01 — iaoaiaoe/iee
aiae?c, Euea?anueeee aea?aeaaiee oi?aa?neoao ?iai? ?aaia O?aiea, Euea?a,
1999.

— oai??? aeeoa?aioe?aeueieo iia?aoi??a. Cie?aia, a oa?i?iao aaeoi??a
aeniiiaioe?aeueiiai oeio iienaii i?inoi?e ei?aiaaeo ooieoe?e ?aaoey?ieo
oa aeayeeo ae?iaeaeaieo ae?ioe/ieo aeeoa?aioe?aeueieo iia?aoi??a.
Iiaoaeiaaii ooieoe?iiaeueia /eneaiiy a ?ioa?iieyoe?eieo eeanao neiaie?a
aeey iia?aoi??a ?c aeene?aoiei niaeo?ii oa u?eueiei i?inoi?ii aaeoi??a
aeniiiaioe?aeueiiai oeio.

Eeth/ia? neiaa: iia?aoi? ?c aeene?aoiei niaeo?ii, aaeoi?
aeniiiaioe?aeueiiai oeio, ooieoe?iiaeueia /eneaiiy, ae?ioe/iee
aeeoa?aioe?aeueiee iia?aoi?.

Aeieo?eoei I. E. Aaeoi?u yeniiiaioeeaeueiiai oeia iia?aoi?ia n
aeene?aoiui niaeo?ii iaae aaiaoiauie i?ino?ainoaaie. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.01 — iaoaiaoe/aneee
aiaeec, Eueaianeee ainoaea?noaaiiue oieaa?neoao eiaie Eaaia O?aiei,
Eueaia, 1999.

.

.

oeaeuo ooieoeee yeniiiaioeeaeueiiai oeia n eiiieaeniuo ia?aiaiiuo.

.

— oai?ee n iiiiuueth aaeoi?ia yeniiiaioeeaeueiiai oeia iienaiu
i?ino?ainoaa ei?iaauo ooieoeee iaeioi?uo eeannia au?iaeaeaiiuo
yeeeioe/aneeo aeeooa?aioeeaeueiuo iia?aoi?ia. A /anoiinoe, iia?aoi?ia,
eioi?ua oa?aeoa?ecothony neeueiui au?iaeaeaieai eo eiyooeoeeaioia
aaeece a?aieoeu (e ia aaneiia/iinoe), a oaeaea iaiauaiiuo
aeeooa?aioeeaeueiuo iia?aoi?ia Eaaeaiae?a.

Iino?iaii ooieoeeiiaeueiia en/eneaiea a eioa?iieyoeeiiiuo eeannao
neiaieia aeey iia?aoi?ia n aeene?aoiui niaeo?ii e ieioiui i?ino?ainoaii
aaeoi?ia yeniiiaioeeaeueiiai oeia.

e i?eaaaeaiu iniiaiua naienoaa ooieoeeiiaeueiiai en/eneaiey. Iino?iai
aeaaa?ae/aneee eciii?oeci ec aeaaa?u neiaieia a aeaaa?o iia?aoi?ia iaae
i?ino?ainoaii ei?iaauo aaeoi?ia caieiooiai iia?aoi?a.

ia yaeythony ooieoeeyie a iau/iii niunea, iiyoiio eniieuecoaony
iiiyoea eioa?iieyoeee, n iiiiuueth eioi?iai ?aaeecoaony oeacaiiue auoa
eciii?oeci.

Iieacaii nouanoaiaaiea caieiooiai ?anoe?aiey ooieoeee io iia?aoi?a n
aeene?aoiui niaeo?ii e ieioiui i?ino?ainoaii aaeoi?ia
yeniiiaioeeaeueiiai oeia a ?aieao ii?aaeaeaiiiai ooieoeeiiaeueiiai
en/eneaiey.

I?eaaaeaiu aiaeiae oai?ai ia ioia?aaeaiee niaeo?a e neiaeiua ooieoeee
io iia?aoi?ia n aeene?aoiui niaeo?ii.

Eeth/aaua neiaa: iia?aoi? n aeene?aoiui niaeo?ii, aaeoi?
yeniiiaioeeaeueiiai oeia, ooieoeeiiaeueiia en/eneaiea, yeeeioe/aneee
aeeooa?aioeeaeueiue iia?aoi?.

Dmytryshyn M. I. Vectors of exponential type of operators with discrete
spectrum on Banach spaces. — Manuscript.

Thesis for obtain the Candidate of Physical and Mathematical degree by
speciality 01.01.01 — mathematical analysis, Ivan Franko Lviv State
University, Lviv, 1999.

— theory of differential operators is given. In particular, the spaces
of root functions of regular elliptic and some of singular elliptic
differential operators are described in terms of exponential type
vectors. The functional calculus in interpolatory classes of symbols
for the operators with discrete spectrum and dense space of the
exponential type vectors is constructed.

Key words: operator with discrete spectrum, vector of exponential type,
functional calculus,ellipticdifferential operator.

I?aeienaii aei ae?oeo 15.04.99 ?. Oi?iao 60o84 1/16. Oi. ae?oe. a?e.1

Iae.-aeae.a?e.1,5. Iaeeaae 100.

Aeae?oeiaaii o aeaeaaie/iio oeaio??

Iaoeiaiai oiaa?enoaa ?i. Oaa/aiea o Eueaia?.

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