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Мультиплікатори Фур’є в просторах Харді в трубчастих областях над відкритими конусами та деякі питання теорії апроксимації: Автореф. дис… канд. фіз.

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IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO I?EEEAAeII? IAOAIAOEEE ? IAOAI?EE

OIANOIE?N Ieaenaiae? Aieiaeeie?iae/

OAeE 517.5

IOEUeOEIE?EAOI?E OO?’? A I?INOI?AO OA?Ae?

A O?OA*ANOEO IAEANOssO IAAe A?AeE?EOEIE EIIONAIE OA AeAssE?
IEOAIIss OAI??? AI?IENEIAOe??

01.01.01 – IAOAIAOE*IEE AIAE?C

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Aeiiaoeuee – 1998

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Aeiiaoeueeiio aea?aeaaiiio oi?aa?neoao?, I?i?noa?noai
ina?oe Oe?a?ie.

Iaoeiaee ea??aiee aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? O?eaoa
?iaeueae Ieoaeeiae/, Aeiiaoeueeee aea?aeaaiee oi?aa?neoao, caa?aeoaa/
eaoaae?e iaoaiaoe/iiai aiae?co oa oai??? ooieoe?e.

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Oaa/oe ?ai? Ieaenaiae?iae/,
Iaoe?iiaeueiee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, caa?aeoaa/ eaoaae?e
iaoaiaoe/iiai aiae?co,

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, noa?oee iaoeiaee ni?a?ia?oiee
Eociaoeiaa Ieueaa ?aai?aia, ?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee
IAI Oe?a?ie, noa?oee iaoeiaee ni?a?ia?oiee a?aeae?eo oai??? ooieoe?e.

I?ia?aeia onoaiiaa

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao, eaoaae?a oai??? ooieoe?e,
I?i?noa?noai ina?oe Oe?a?ie, Aei?i?iiao?ianuee.

Caoeno a?aeaoaeaoueny “_19_” aa?aciy 1999 ?. i _15_ aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 11.193.01 i?e ?inoeooo?
i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie ca aae?anith: 340114,
i.Aeiiaoeuee, aoe. ?.Ethenaiao?a, 74.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? ?inoeoooa
i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie ca aae?anith: 340114,
i.Aeiiaoeuee, aoe. ?.Ethenaiao?a, 74.

Aaoi?aoa?ao ?ic?neaiee “_17_” _ethoiai_ 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee

Eiaaeaanueeee I.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

ia i?ain? oe?eeie ooieoe?yie ne?i/aiiiai i?anoaiaiy.

) ieoaiiy i?i ioeueoeie?eaoi? iia’ycaia c iiaeeea?noth cia?aaeaiiy
ooieoe??-ioeueoeie?eaoi?a o aeaeyae? ia?aoai?aiiy Oo?’? ne?i/aiii?
ai?ae?anueei? i??e. Caaaeuei? oaeoe, ui noinothoueny ioeueoeie?eaoi??a
Oo?’? oa ?o canoinoaaiiy, aeeeaaeai? o a?aeiieo iiiia?ao?yo A.C?aioiaea,
?.Noaeia, ?.Noaeia oa A.Aaena, ?.Aaeaa?aena.

Aei oai??? iaaeeaeaiiy ooieoe?e ioeueoeie?eaoi?e canoiniaoaaee
A.N.I?oya?i, N.I.Oaeyeianueeee, ?.I.O?eaoa, A.N.Aae?inueeee oa ?i.

, iauiaeaaii iaea?aeai? ?.I.O?eaoaii).

io?eiai? N.A.I?oe?iei oa E.Ouei?iaiaea?ii.

, a aa?oi?e i?aieiuei? oa ?o canoinoaaiith i?enay/aii aeena?oaoe?th
I.I.Nieyi?ea).

iaea?eueo caaaeueieie iaeanoyie ? naia o?oa/ano? iaeano? iaae
a?aee?eoeie eiionaie.

ooieoe?iiae?a ia?e i?inoi??a aeaaeeeo ooieoe?e oa ?i.

ooieoe?iiaee aeey ia?e i?inoi??a aeaaeeeo ooieoe?e ? iiaeoeyie
aeaaeeino?. A e?aoiiio aeiaaeeo aeey io?eiaiiy iio??aieo ioe?iie
aeiaiaeeoueny aaiaeeoe iia? niaoe?aeuei? iiaeoe? aeaaeeino?.

ia a?ae??ceo ae?enii? a?n? c o?aooaaiiyi iieiaeaiiy oi/ee) iauiaeaaii
?ica’ycaii a aneiioioe/ii oi/i?e oi?i? ?.I.O?eaoaii). O aeiaaeeo i?ain?
oey caaea/a caeeoaeanue ia ?ica’ycaiith. Ua N.I.Aa?iooaei iieacaa, ui a
oeueiio aeiaaeeo o?aaa iaaeeaeoaaoe oe?eeie ooieoe?yie ne?i/aiiiai
i?anoaiaiy, a i?yi? oa iaa?iai? oai?aie iaea?aeaii aaea aeineoue aeaaii
TH.A.A?oaeiei. Inoaii?ie ?ieaie c’yaeeenue iia? i?aeoiaee a oeueiio eie?
i?iaeai.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa
aeeiioaaeanue o iaaeao aea?aeathaeaeaoieo iaoeiaeo oai A.86.50.1/4.14
“Oai??y iia?aoi??a ? eiiieaeniee aiae?c” oa ? 0196 UKRAINE 007096
“Aa?iii?/iee aiae?c ooieoe?e oa iia?aoi??a”.

Iaoa ? caaea/? aeine?aeaeaiiy.

oa aeine?aeeoe ?oi? iniiai? aeanoeaino?.

Io?eiaoe aoaeoeai? aeinoaoi? oiiae aeey ioeueoeie?eaoi??a. Aeine?aeeoe
iaaio oi/i?noue io?eiaieo aeinoaoi?o oiia oeyoii io?eiaiiy aeayeeo
iaiao?aeieo.

ooieoe?iiaeo ia?e i?inoi??a, ui caaeathoueny iie?aa?iii?/iei
iia?aoi?ii, a oaeiae aeiaanoe aea?aaeaioi?noue aeaio iiaeoe?a aeaaeeino?
a i?inoi?ao Oa?ae? a aa?oi?e i?aieiuei?.

ia i?ain? oe?eeie ooieoe?yie ne?i/aiiiai i?anoaiaiy c o?aooaaiiyi
iieiaeaiiy oi/ee.

ia i?ain? oe?eeie ooieoe?yie ne?i/aiiiai i?anoaiaiy aeei?enoiao?oueny
iaoiae niaoe?aeueieo cia?aaeaiue ooieoe??.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a.

oa aeine?aeaeai? ?oi? iniiai? aeanoeaino?.

? anoaiiaeaii iaaio oi/i?noue oeeo oiia.

).

ooieoe?iiae ia?e i?inoi??a, ui caaeathoueny iie?aa?iii?/iei iia?aoi?ii,
aeiaaaeaii aea?aaeaioi?noue aeaio ??cieo iiaeoe?a aeaaeeino?.

Ne?ae a?aecia/eoe, ui iniiai? ?acoeueoaoe ? ?noioii aaaaoiaei??ieie,
oiaoi ia ? i?inoei ia?aianaiiyi iaeiiaei??ieo ?acoeueoao?a, iaeiae,
iaa?oue aeey iaeiiaei??iiai aeiaaeeo aiie ? iiaeie.

ia i?ain? oe?eeie ooieoe?yie ne?i/aiiiai i?anoaiaiy c o?aooaaiiyi
iieiaeaiiy oi/ee. Oaeei /eiii iiai?noth ?ica’ycaii a?aeiio aeno?aiaeueio
caaea/o.

Oai?aoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Iaea?aeai? a aeena?oaoe??
?acoeueoaoe iathoue oai?aoe/ia cia/aiiy. Aiie iiaeooue aooe canoiniaai?
a aa?iii?/iiio aiae?c? oa oai??? ai?ieneiaoe??.

ooieoe?iiaee aeey ia?e i?inoi??a, ui caaeathoueny ??cieie
aeeoa?aioe?aeueieie iia?aoi?aie ae?ioe/iiai oeio ? o. ?i. Ne?ae
cacia/eoe oaeiae, ui ca aeiiiiiaith oeeo ?acoeueoao?a iiaeia i?iaiaeeoe
ioe?iee c o?aooaaiiyi aaiiao??? eiiona, yeee ? iniiaith ?icaeyaeoaaii?
o?oa/anoi? iaeano?.

ia i?ain?, iiaeia aeei?enoiaoaaoe oaeiae aeey io?eiaiiy iiae?aieo
aneiioioe/ii oi/ieo ioe?iie a ?ioeo caaea/ao oai??? ai?ieneiaoe??.

Iniaenoee aianie caeiaoaa/a. An? ?acoeueoaoe aeena?oaoe?? iaeaaeaoue
aaoi?o, iaeiae aeaye? c ieo iioae?eiaai? a ?iaioao c? ni?aaaoi?aie. A
?iaio? [3] aaoi?o iaeaaeeoue oai?aia 3 (aeiaaeie i?aieiueie), ui
cacia/aii a oaeno? noaoo?. A ?iaio? [4] aaoi?o iaeaaeeoue oai?aia 4
(iaaeeaeaiiy ia i?ain?), ui oaeiae cacia/aii a oaeno? noaoo?. A ?iaio?
[6] aaoi?ii aiiiniaaia oai?aia 2, ui aeiaaaeaia a [4].

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Ie?ai? ?acoeueoaoe aeena?oaoe??
aeiiia?aeaeenue ia I?aeia?iaei?e eiioa?aioe?? “Oai??y iaaeeaeaiiy oa
caaea/? ia/enethaaeueii? iaoaiaoeee” (Aei?i?iiao?ianuee, 1993 ?.), ??
oeie? “?yaee Oo?’?: oai??y ? canoinoaaiiy” (Eai’yiaoeue-Iiae?euenueeee,
1997 ?.), iaoeiaeo eiioa?aioe?yo i?ioani?nueei-aeeeaaeaoeueeiai neeaaeo
Aeiiaoeueeiai aea?aeaaiiai oi?aa?neoaoo (Aeiiaoeuee, 1995 oa 1997 ??.),
I?aeia?iaei?e eiioa?aioe?? “Oai?ey i?eaeeaeaiee e aa?iiie/aneee aiaeec”
(Ooea, 1998 ?.).

A oe?eiio aeena?oaoe?y aeiiia?aeaeanue ia nai?ia?? i?ioani?a ?.I.Oaa/oea
(Iaoe?iiaeueiee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, 1998 ?.), nai?ia??
i?ioani??a A.I.Iioi?iiai oa A.O.Aaaaiea (Aei?i?iiao?ianueeee aea?aeaaiee
oi?aa?neoao, 1998 ?.), nai?ia?? i?ioani?a ?.I.O?eaoaa (Aeiiaoeueeee
aea?aeaaiee oi?aa?neoao, 1993 – 1998 ??.).

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a 10 ?iaioao,
c yeeo 5 – noaoo? a iaoeiaeo aeaeaiiyo, 5 – oace aai iaoa??aee
aeiiia?aeae eiioa?aioe?e.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa aeeeaaeaia ia 137
noi??ieao ? i?noeoue ia?ae?e oiiaieo nei?i/aiue, anooi, iniiaio /anoeio
c aeaio ?icae?e?a, aeniiaee oa nienie e?oa?aoo?e, ui neeaaea?oueny c 57
aeaea?ae ? ?icoaoiaaiee ia 8 noi??ieao.

INIIAIEE CI?NO AeENA?OAOe??

O anooi? iaa?oioiao?oueny aeooaeuei?noue aeine?aeaeaiue, iaeyae ?ia?o o
aeaiiio iai?yieo, noenei iaaaaeaii ci?no ?iaioe oa noi?ioeueiaaii
iniiai? ?? ?acoeueoaoe.

. Io?eiai? ?acoeueoaoe ? ?noioii aaaaoiaei??ieie (oea aeaeii ye c
oi?ioethaaiue, oae ? c aeiaaaeaiue), aea iaa?oue o iaeiiaei??iiio
aeiaaeeo (aeiaaeie aa?oiuei? i?aieiueie) aiie ? iiaeie.

. Aeey ei?aeoiiai aaaaeaiiy oeueiai iiiyooy aeiaiaeeoueny oaea oai?aia.

?nio? a oa?i?iao oai??? ocaaaeueiaieo ooieoe?e iia?eueiiai c?inoaiiy),
oiaoi

.

):

,

ii?i?)).

:

, aoaeaii iaceaaoe ooieoe?th:

– ii?i?)).

E??i oiai, ia? i?noea oaea oi?ioea iaa?iaiiy:

).

Aeae? aaaaeaii icia/aiiy ioeueoeie?eaoi?a Oo?’? oa iaaaaeaii aeaye? eiai
aeanoeaino?.

?

.

a oeueiio icia/aii? aecia/a?oueny iaeiicia/ii:

,

ui ?iaeoue icia/aiiy ioeueoeie?eaoi?a iaaecae/aeii i?e?iaeiei.

( 1.2. i?noeoue o nia? iaiao?aei? aeey iiaeaeueoiai aeiiii?aei?
?acoeueoaoe, a oaeiae iaaiai?aiiy iniaeeainoae i?inoi??a Oa?ae? a
o?oa/anoeo iaeanoyo iaae a?aee?eoeie eiionaie, ?o a?aei?iiino? a?ae
a?aeiia?aeieo i?inoi??a a e?oc? (aai iaeanoyo ?aeioa?oa).

Iniiai? ?acoeueoaoe ?icae?eo i?noyoueny a ( 1.3., aea iaaaaeaii
aeinoaoi? oa aeaye? iaiao?aei? oiiae aeey ioeueoeie?eaoi??a. Iniiaith
ooo ? ianooiia oai?aia, ui aea? c?o/io aeey ia?aa??ee aeinoaoith oiiao
ioeueoeie?eaoi?a.

?

,

,

.

aoei iaea?aeaii I.I.Nieyi?eii. O aeiaaeeo i?inoi??a Oa?ae? a iie?e?oc?
oaea oai?aia iaeaaeeoue ?.I.O?eaoao, a a a?eueo caaaeueiiio aeiaaeeo
iaeanoae ?aeioa?oa – A?o.A.Aie/eiao.

).

a aeayeiio ci?no? ? oaeiae iaiao?aeiith.

.

Aeae? aeiaiaeeoueny e?eoa??e ioeueoeie?eaoi?a aeey ?aae?aeueii?
ooieoe??, yeee ciiao i?aee?aneth? oi/i?noue oai?aie 1.2.

.

? aac i?eiouaiiy ?? o?i?oiino?.

.

,

aea

,

?

.

.

.

oa aeniiiaioe?eiiai niaaeaiiy ooieoe?? ? an?o ?? iio?aeieo.

).

Ae?oaee ?icae?e i?enay/aii aeayeei caaea/ai oai??? ai?ieneiaoe??. A
( 2.1. io?eiaii aeainoi?iii? ioe?iee oaeaeeino? iaaeeaeaiiy ooieoe??
na?aaei?ie Aioia?a-??nna ?? ?ioaa?aeo Oo?’?:

ooieoe?iiaeo ia?e i?inoi??a, ui caaeathoueny iie?aa?iii?/iei
iia?aoi?ii:

.

Aeey oeueiai, iiae?aii aei aeiaaeeo ioeueoeie?eaoi??a noaiaiaaeo ?yae?a,
aaiaeeoueny niaoe?aeueiee iiaeoeue aeaaeeino?:

).

).

.

)).

Caoaaaeeii, ui iiae?ai? ioe?iee iiaeia io?eiaoe ? aeey ?ioeo
aeeoa?aioe?aeueieo iia?aoi??a.

). Iaoiae ioeueoeie?eaoi??a canoiniao?oueny aeey aeiaaaeaiiy
aea?aaeaioiino? iaeiiai ei?eniiai iiaeoey aeaaeeino? cae/aeiiio
eiioo?iiio. C oeei iiaei e?iaa?eciaaiei iiaeoeai aeaaeeino?:

,

? a?i iiaea aooe canoiniaaiee aei io?eiaiiy ??cieo ioe?iie,
iai?eeeaae, aiaeiao oai?aie Oa?ae?-E?ooeueaoaea ? o. ?i. Iniiaiei
?acoeueoaoii ( 2.2. ? ianooiia oai?aia.

)).

th iio?aeiith) oe?eeie ooieoe?yie ne?i/aiiiai i?anoaiaiy c o?aooaaiiyi
iieiaeaiiy oi/ee. Iniiaiei ?acoeueoaoii oeeo aeine?aeaeaiue ? ianooiia
oai?aia.

oaea, ui

.

, ui i?e iaaeeaeaii? aei ioey aea? e?auo ioe?ieo iaaeeaeaiiy, a ia
iane?i/aiiino? – c?inoath/ee /eai. Caoaaaeeii, ui oaeiai ?iaeo ioe?iee ?
i?aaeeueieie, ye iii?oea ua N.I.Aa?iooaei.

oe?eeie ooieoe?yie aeniiiaioe?aeueiiai oeio oa ianooiii? oai?aie.

oaea, ui

.

ia? i?noea ia??ai?noue:

,

.

AENIIAEE

, aeine?aeaeaii ?oi? iniiai? aeanoeaino?.

Io?eiaii aoaeoeai? aeinoaoi? oa aeaye? iaiao?aei? oiiae aeey
ioeueoeie?eaoi??a o aeacaieo i?inoi?ao. Io?eiai? ?acoeueoaoe ? ?noioii
aaaaoiaei??ieie (iaa?oue i?inoaaeaia caeaaei?noue a?ae aaiiao???
eiiona), oi/a ? a iaeiiaei??iiio aeiaaeeo i?inoi??a Oa?ae? a aa?oi?e
i?aieiuei? aiie ? iiaeie.

ooieoe?iiaeo ia?e i?inoi??a, ui caaeathoueny iie?aa?iii?/iei
iia?aoi?ii.

Oe? ae aeinoaoi? oiiae aeicaieeee aeiaanoe aea?aaeaioi?noue aeaio
iiaeoe?a aeaaeeino? a i?inoi?ao Oa?ae? a aa?oi?e i?aieiuei?.

oe?eeie ooieoe?yie ne?i/aiiiai i?anoaiaiy c o?aooaaiiyi iieiaeaiiy
oi/ee.

NIENIE IIOAE?EIAAIEO I?AOeUe CA OAIITH AeENA?OAOe??

e eo i?eiaiaiea a oai?ee aii?ieneiaoeee // Aeiiia?ae? IAI Oe?a?ie. –
1997. – ? 5. – N. 49-53.

Tovstolis A.V. Fourier multipliers in Hardy spaces in tube domains over
open cones and their applications // Methods of functional analysis and
topology. – 1998. – Vol. 4. – ? 1. – P. 68-89.

Oianoieen A.A., O?eaoa ?.I. Yeaeaaeaioiinoue ?aciuo iiaeoeae aeaaeeinoe
a i?ino?ainoaao Oa?aee // Oai?ey i?eaeeaeaiey ooieoeee. O?oaeu Einoeoooa
i?eeeaaeiie iaoaiaoeee e iaoaieee IAI Oe?aeiu. – O. 3. – Aeiiaoee: EIII
IAIO. – 1998. – N. 201-210.

O?eaoa ?.I., Eo?aaineay A.I., Oianoieen A.A. I i?eaeeaeaiee ooieoeee
aeaaa?ae/aneeie iieeiiiaie e oeaeuie ooieoeeyie // A?niee Aeiiaoeueeiai
oi?aa?neoaoo. – 1997. – ? 1. – N. 49-55.

// A?niee Aeiiaoeueeiai oi?aa?neoaoo. – 1998. – ? 1. – N. 42-48.

Oianoieen A.A., O?eaoa ?.I. Iioi/a/iia i?eaeeaeaiea iieeiiiaie ia
io?acea e oeaeuie ooieoeeyie ia aiaoiinoe io?acea e iieoine // Oai??y
iaaeeaeaiiy oa caaea/? ia/enethaaeueii? iaoaiaoeee. Oace aeiiia?aeae. –
Aei?i?iiao?ianuee: AeAeO. – 1993. – N.183.

e i?eaeeaeaiea n?aaeieie Aioia?a-?enna eioaa?aeia Oo?uea // Oacenu
aeieeaaeia iao/iie eiioa?aioeee i?ioanni?nei-i?aiiaeaaaoaeueneiai
ninoaaa Aeiiaoeeiai ainoaea?noaaiiiai oieaa?neoaoa (a.Aeiiaoee, ai?aeue
1995 a.). – Aeiiaoee: AeiiAO. – 1995. – N. 189-190.

e eo i?eiaiaiea a oai?ee aii?ieneiaoeee // Iaoa??aee aoc?anueei?
iaoeiai? eiioa?aioe?? i?ioani?nueei-aeeeaaeaoeueeiai neeaaeo ca
i?aenoieaie iaoeiai-aeine?aeieoeueei? ?iaioe: iaoaiaoeea, o?ceea,
aeieia?y (Aeiiaoeuee, ea?oaiue 1997 ?.). – Aeiiaoeuee: AeiiAeO. – 1997.
– N. 38-42.

e eo i?eiaiaiea a oai?ee aii?ieneiaoeee // ?? oeiea “?yaee Oo?’?:
oai??y ? canoinoaaiiy” (Eai’yiaoeue-Iiae?euenueeee, 30 /a?aiy – 5 eeiiy
1997 ?.). Oace aeiiia?aeae. – Ee?a. – 1997. – N. 126-127.

Oianoieen A.A. Ia?aaainoai oeia Oa?aee-Eeooeueaoaea e ?aciua iiaeoee
aeaaeeinoe a i?ino?ainoaao Oa?aee a aa?oiae iieoieineinoe //
Iaaeaeoia?iaeiay eiioa?aioeey “Oai?ey i?eaeeaeaiee e aa?iiie/aneee
aiaeec” (?inney, Ooea, 26-29 iay 1998 a.). Oacenu aeieeaaeia. – Ooea:
OoeAO. – 1998. – N. 258-259.

AIIOAOe??

Oianoie?n I.A. Ioeueoeie?eaoi?e Oo?’? a i?inoi?ao Oa?ae? a o?oa/anoeo
iaeanoyo iaae a?aee?eoeie eiionaie oa aeaye? ieoaiiy oai???
ai?ieneiaoe??. – ?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. – ?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie,
Aeiiaoeuee, 1999.

th iio?aeiith ia ae?eni?e i?ain? oe?eeie ooieoe?yie ne?i/aiiiai
i?anoaiaiy c o?aooaaiiyi iieiaeaiiy oi/ee. ?acoeueoaoe iathoue
oai?aoe/ia cia/aiiy ? iiaeooue aooe canoiniaai? a aa?iii?/iiio aiae?c?
oa oai??? ai?ieneiaoe??.

ooieoe?iiae, iiaeoeue aeaaeeino?, oe?ea ooieoe?y ne?i/aiiiai
i?anoaiaiy.

Tovstolis A.V. Fourier multipliers in Hardy spaces in tube domains over
open cones and some questions of the approximation theory. – Manuscript.

Thesis for a candidate’s degree (physical and mathematical sciences) by
speciality 01.01.01 – mathematical analysis. – Institute of Applied
Mathematics and Mechanics of National Academy of Sciences of Ukraine,
Donetsk, 1999.

th derivative on a real half-axis by entire functions of bounded
half-degree with regard to position of a point is obtained. The results
are theoretical and can be applied to harmonic analysis and
approximation theory.

functional, modulus of smoothness, entire function of bounded
half-degree.

Oianoieen A.A. Ioeueoeieeeaoi?u Oo?uea a i?ino?ainoaao Oa?aee a
o?oa/aouo iaeanoyo iaae ioe?uouie eiionaie e iaeioi?ua aii?inu oai?ee
aii?ieneiaoeee. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/?iie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.01 – iaoaiaoe/aneee
aiaeec. – Einoeooo i?eeeaaeiie iaoaiaoeee e iaoaieee IAI Oe?aeiu,
Aeiiaoee, 1999.

aeey eco/aiey eiino?oeoeee eeanne/aneiai aa?iiie/aneiai aiaeeca.

Aeey ooieoeee ec ?anniao?eaaaiuo i?ino?ainoa Oa?aee iieo/aia oi?ioea
ia?auaiey aeey i?aia?aciaaiey Oo?uea, ni?aaaaeeeaay anthaeo a aeaiiie
o?oa/aoie iaeanoe, /oi iicaieyao anoanoaaiii ii?aaeaeeoue
ioeueoeieeeaoi?, ?anniio?aoue ?acee/iua n?aaeiea eioaa?aea Oo?uea, yaii
auienuaaoue oi?ioeu aeey ?acee/iuo aeeooa?aioeeaeueiuo iia?aoi?ia e o.i.

A ?aaioa iieo/aiu yooaeoeaiua aeinoaoi/iua oneiaey aeey oiai, /oiau
ooieoeey ii?aaeaeyea ioeueoeieeeaoi? a oeacaiiuo i?ino?ainoaao. I?e yoii
ii?aaeaeaia iaeioi?ay caaeneiinoue io aaiiao?ee ioe?uoiai eiiona.
Oi/iinoue iieo/aiiuo aeinoaoi/iuo oneiaee iiaeoaa?aeaeatho iaeioi?ua
iaiaoiaeeiua oneiaey, oaeaea iieo/aiiua a ianoiyuae ?aaioa.

ooieoeeiiaea ia?u i?ino?ainoa, caaeaaaaiuo iieeaa?iiie/aneei
iia?aoi?ii. Aeey yoeo oeaeae aaiaeeony niaoeeaeueiue iiaeoeue
aeaaeeinoe. Aeinoaoi/iua oneiaey oaeaea i?eiaiaiu aeey onoaiiaeaiey
yeaeaaeaioiinoe aeaoo ?aciuo iiaeoeae aeaaeeinoe (yoa caaea/a ?aoaaony
oieueei aeey iaeiiia?iiai neo/ay eae aeaiiino?aoeey iaoiaea).

.

Iniiaiua ?acoeueoaou yaeythony nouanoaaiii iiiaiia?iuie, ii aeaaea a
iaeiiia?iii neo/aa i?ino?ainoa Oa?aee a aa?oiae iieoieineinoe iie
yaeythony iiauie.

ia anae ine oeaeuie ooieoeeyie yeniiiaioeeaeueiiai oeia eiaaony oi/iay
ioeaiea iaeeo/oaai i?eaeeaeaiey (ecaanoiay oai?aia Aoeaca?a-E?aeia).
Aneiioioe/anee oi/iua ioeaiee i?eaeeaeaiey ooieoeee aeaaa?ae/aneeie
iieeiiiaie ia io?acea iieo/aiu iaaeaaii ?.I.O?eaoaii. A neo/aa iieoine
aii?in inoaaaeny ioe?uoui, oioy i?yiua e ia?aoiua oai?aiu aac oi/iuo
eiinoaio iieo/aiu oaea aeiaieueii aeaaii TH.A.A?oaeiui. A aeenna?oaoeee
yoa caaea/a ?aoaia – iieo/aia aneiioioe/anee oi/iay ioeaiea
i?eaeeaeaiey.

A ?aaioa eniieuecothony ?acee/iua iaoiaeu aa?iiie/aneiai aiaeeca, oai?ee
aii?ieneiaoeee, iiiaiia?iiai eiiieaeniiai aiaeeca. Iaoiae
ioeueoeieeeaoi?ia i?eiaiyaony aeey iieo/aiey oi/iuo aeaonoi?iiieo
ioeaiie i?eaeeaeaiey. Ioeaiee i?eaeeaeaiey ooieoeee ia iieoine oeaeuie
ooieoeeyie eiia/iie iieonoaiaie iieo/aiu n eniieueciaaieai iaoiaea
niaoeeaeueiuo i?aaenoaaeaiee ooieoeee.

?acoeueoaou iinyo oai?aoe/aneee oa?aeoa? e iiaoo auoue eniieueciaaiu a
aa?iiie/aneii aiaeeca e oai?ee aii?ieneiaoeee.

ooieoeeiiae, iiaeoeue aeaaeeinoe, oeaeay ooieoeey eiia/iie iieonoaiaie.

e aii?ieneiaoeaiua naienoaa iaoiaeia noiie?iaaiey noaiaiiuo ?yaeia //
Aeiee. Aeaae. Iaoe. – 1994. – O. 335. – ? 6. – N. 697-699.

) by certain means of Fourier integrals // Analysis Mathematica. –
1986. – ? 12. – P. 59-75.

) Oae? caaea/? ?icaeyaeathoueny i?ney oiai, ye N.I.I?eieuenueeee iii?oea
aoaeo iie?ioaiiy iaaeeaeaiiy a?ey e?ioe?a a?ae??ceo.

) O?eaoa ?.I. I?yiua oai?aiu i i?eaeeaeaiee aeaaa?ae/aneeie iieeiiiaie
aeaaeeeo ooieoeee ia io?acea // Iaoai. caiaoee. – 1993. – O. 54. –
? 6. – N. 113-121.

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