Швидкості збіжності рядів Тейлора і рядів Фабера на класах psi—інтегралів функцій комплексної змінної: Автореф. дис… канд. фіз.-мат. наук / В.В. Са

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

?INOEOOO IAOAIAOEEE

NAA*OE A?eoi? Aaneeueiae/

OAeE 517.5

OAEAeEINO? CA?AEIINO? ?ssAe?A OAEEI?A

–?IOAA?AE?A

OOIEOe?E EIIIEAENII? CI?III?

01.01.01.— iaoaiaoe/iee aiae?c.

Aaoi?aoa?ao aeena?oaoe??

ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei—iaoaiaoe/ieo iaoe

Ee?a –1998

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia a ?inoeooo? iaoaiaoeee IAI Oe?a?ie

Iaoeiaee ea??aiee: /eai—ei?aniiiaeaio IAI Oe?a?ie,

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

NOAIAIAOeUe Ieaenaiae? ?aaiiae/,

?inoeooo iaoaiaoeee IAI Oe?a?ie,

caa. a?aeae?eii oai??? ooieoe?e.

Io?oe?ei? iiiiaioe :

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

AI?AA*OE Ie?ineaa Eueaiae/,

?inoeooo iaoaiaoeee IAI Oe?a?ie, caa. a?aeae?eii

aeeoa?aioe?aeueieo ??aiyiue a /anoeiieo iio?aeieo;

eaiaeeaeao o?ceei — iaoaiaoe/ieo iaoe,

aeioeaio Ae?ICAe Ay/aneaa Aieiaeeie?iae/,

Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao

Oe?a?ie (EI?),eaoaae?a iaoaiaoeee N 1.

I?ia?aeia onoaiiaa: Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao,
eaoaae?a oai??? ooieoe?e.

Caoeno a?aeaoaeaoueny «2» ethoiai 1999 ?. 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, INI, aoe.
Oa?auaie?anueea,3

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? ?inoeoooo iaoaiaoeee
IAI Oe?a?ie

Aaoi?aoa?ao ?ic?neaii “23” a?oaeiy 1998 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? ?aaee

aeieoi? o?c—iao. iaoe
N.A. Ia?aaa?c?a

Caaaeueia oa?aeoa?enoeea ?iaioe

.

(. Cie?aia, ciaeaeaii ?ica’ycee caaea/? Eieiiai?iaa — I?eieuenueeiai, a
oaeiae iaea?aeaii aiaeia a?aeiii? ia??aiino? Eaaaaa.

Aeeeeea? i?e?iaeiee ?ioa?an caaea/a i?i iioe?aiiy oeeo ?acoeueoao?a ia
eiiieaenio iaeanoue, a naia, ia ?yaee Oaeei?a oa ?o ocaaaeueiaiiy —
?yaee Oaaa?a.

Aeine?aeaeaiiy o oeueiio iai?yieo ? i?iaeiaaeaiiyi aeine?aeaeaiue,
i?iaaaeaieo A.Eaiaeao, N.A.No?/e?iei, E.A.Oaeeiaei, I.E.No?o?iei,
I.?.Noaiaioeai, A.N.?iiaitheii oa ?ioeie iaoaiaoeeaie.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie,oaiaie.

?iaioa i?iaiaeeeanue ca?aeii c caaaeueiei ieaiii aeine?aeaeaiue
a?aeae?eo oai??? ooieoe?e ?inoeoooo iaoaiaoeee IAI Oe?a?ie.

-iaoiaeii i?aenoiiaoaaiiy

.

, a naia, anoaiiaeoe aneiioioe/i? ??aiino? aeey aa?oi?o a?aiae caeeoe?a
?yae?a Oaeei?a, a oaeiae io?eiaoe aiaeia ia??aiino? Eaaaaa-Eaiaeao.

, /anoeiieie noiaie ?o ?-oaaa?iaeo ?yae?a.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Iniiai? ?acoeueoaoe
aeena?oaoe?? ? iiaeie. Aei ieo a?aeiinyoueny:

.

-?ioaa?ae?a.

-?ioaa?ae?a.

4. Aiaeia oai?aie i?i na?aaei? aeey aiae?oe/ieo ooieoe?e.

a?ae /anoeiieo noi ?o ?-oaaa?iaeo ?yae?a.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Iaea?aeai? ?acoeueoaoe
iathoue oai?aoe/iee oa?aeoa? ? iiaeooue aooe canoiniaaieie aeey
iiaeaeueoiai ?icaeoeo oai??? iaaeeaeaiiy ooieoe?e.

Iniaenoee aianie caeiaoaa/a. Iinoaiiaea caaea/ iaeaaeeoue iaoeiaiio
ea??aieeia?. Iniiai? ?acoeueoaoe io?eiaii aaoi?ii naiino?eii.

Ai?iaaoe?y ?acoeueoao?a ?iaioe. Iniiai? ?acoeueoaoe aeiiia?aeaeeny ia:

— nai?ia?ao a?aeae?eo oai??? ooieoe?e ?inoeoooo iaoaiaoeee IAI Oe?a?ie;

— ia’?aeiaiiio nai?ia?? c oai??? ooieoe?e (?inoeooo iaoaiaoeee IAI
Oe?a?ie);

— ae?oa?e iaoaiaoe/i?e oeie? “?yaee Oo?’?: oai??y ? canoinoaaiiy”
(Oe?a?ia, i.Eai’yiaoeue-Iiae?euenueeee, 30 /a?aiy — 5 eeiiy 1997 ?.).

Ioae?eaoe??. Ii oai? aeena?oaoe?? iioae?eiaaii 5 ?ia?o.

Nienie iioae?eiaaieo ?ia?o iaaaaeaii ieae/a.

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny c? anooio, o?ueio
?icae?e?a, ui i?noyoue 14 ia?aa?ao?a, nieneo iniiaieo iicia/aiue oa
nieneo oeeoiaaii? e?oa?aoo?e, ui i?noeoue 64 iaeiaioaaiiy. Ianya ?iaioe
neeaaea? 125 noi??iie iaoeiiieniiai oaenoo.

Iniiaiee ci?no aeena?oaoe??

O anooi? iaa?oioiaaii aeooaeuei?noue ? aaaeeea?noue ieoaiue, ui
?icaeyaeathoueny a aeena?oaoe??, i?iaaaeaii noeneee iaeyae aeecueeeo ca
iai?yieii ?ia?o, noi?ioeueiaaia iaoa aeine?aeaeaiue oa ?o iiaecia,
aeeeaaeaii ci?no ?iaioe ca ?icae?eaie.

— p-oaaa?ia? iiiai/eaie.

).

)+.

oa ?o ia?aoi?ioethaaiiyi o c?o/i?e aeey ian oi?i?. Aeey iiaiioe oe?
oaa?aeaeaiiy noi?iaiaeaeothoueny ei?ioeeie ni?iuaieie aeiaaaeaiiyie.

.

, yeui

(|k|)) ckeikt,

?

ckeikt,

f.

((A).

) ? cai?oeaie ca Aecyaeeeii ?ioaa?ae?a oeio Eio? a iaeano? G c yae?aie

.

.

iinoaaeii o a?aeiia?aei?noue iiiai/eai

.

. Iieeaaeaii

, (1)

.

.

A i?eeiyoeo iicia/aiiyo ia? i?noea oaea

, icia/aii? oi?ioeaie (1), ? oaeeie, ui ?o ia?aoai?aiiy Oo?’?

,

ia? i?noea ??ai?noue

(,

(2)

.

Iieeaaeaii

.

aeeiio?oueny ??ai?noue (2), a ye?e

;

aeeiio?oueny ??ai?noue (2), a ye?e

.

.

niaaeieo aei ioey ooieoe?e;

,

,

.

(

X aeaaa?a?/ieie iiiai/eaiaie noaiaiy 0 oaea, ui

( .

ia??ai?noue (11) iaaoaea aeaeyaeo

(12)

sseui i?e oeueiio

(,

ni?aiaaea? c ioe?ieith, aeiaaaeaiith I.?.Noaiaioeai ? A.N.?iiaitheii.

? ?-oaaa?iaith.

aeeiio?oueny oiiaa

,

aea N — eiinoaioa, ui iiaea caeaaeaoe o?eueee a?ae e?eai? A.

Aeey ?-oaaa?iaeo iaeanoae ni?aaaaeeeaa aeeth/aiiy

,

a oaeiae ianooiia oaa?aeaeaiiy.

, ooieoe?y

? aeeiio?oueny ia??ai?noue

,

aea

(13)

eaaei io?eiaoe a?aeiia?aei? ?acoeueoaoe ? aeey ?yae?a Oaaa?a.

Iaaaaeaii iaeei c ?acoeueoao?a (2.

, aeeiio?oueny ia??ai?noue

(,

aea

N — eiinoaioa, ui aecia/a?oueny ??ai?noth (13), I(1) — aaee/eia,
??aiii??ii iaiaaeaia a?aeiinii f ? n.

Aeniiaee

1.Ciaeaeaii ?ioaa?aeuei? cia?aaeaiiy a?aeoeeaiue
aeaaa?a?/ieo iiiai/eai?a,

ui ii?iaeaeothoueny e?i?eieie iaoiaeaie i?aenoiiaoaaiiy p-oaaa?iaeo
?yae?a a?ae

-?ioaa?ae?a ooieoe?e, aiae?oe/ieo a iaeano? G.

-?ioaa?ae?a.

-?ioaa?ae?a.

4.Aeiaaaeaii aiaeia oai?aie i?i na?aaei? aeey aiae?oe/ieo
ooieoe?e.

-?ioaa?ae?a ooieoe?e, aiae?oe/ieo a iaeano? G, a?ae /anoeiieo noi ?o
p-oaaa?iaeo ?yae?a

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

1. Naa/oe A.A. Aei oai?aie i?i na?aaei? aeey aiae?oe/ieo ooieoe?e //
Oe?. iao. aeo?i. — 1997. — 49, ?8. — N.1143-1147.

2. Naa/oe A.A. Aneiioioeea caeeoeo ?yaeo Oaeei?a aeey aiae?oe/ieo
ooieoe?e // ?yaee Oo?’?: oai??y ? canoinoaaiiy / I?aoe? ?i-oo iaoaiaoeee
IAI Oe?a?ie. — 1998. — 20. — N.263-279.

3. Naa/oe A.A. Iiaaae?iea caeeoeo ?yaeo Oaeei?a ia eeanao oe?eeo
ooieoe?e // ?yaee Oo?’?: oai??y ? canoinoaaiiy / I?aoe? ?i-oo iaoaiaoeee
IAI Oe?a?ie. -1998.-20.-N.280-285.

4. Naa/oe A.A. Oaeaee?noue ca?aeiino? ?yaeo Oaeei?a aeey aeayeeo eean?a
aiae?oe/ieo ooieoe?e // Oe?. iao. aeo?i. — 1998. — 50, ?7. —
N.1001-1003.

noiaie Oaaa?a a aei?aeaiiaeo iaeanoyo // ?? oeiea “?yaee Oo?’?: oai??y
? canoinoaaiiy” (Eai’yiaoeue-Iiae?euenueeee, 30 /a?aiy-5 eeiiy 1997 ?.):
Oace aeii. — Ee?a, 1997.-N.112-113.

-?ioaa?ae?a ooieoe?e eiiieaenii? ci?iii?”.

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 iaoaiaoeee IAI Oe?a?ie, Ee?a 1998.

, a oaeiae aiaeia ia??aiino? Eaaaaa-Eaiaeao.

, a?ae /anoeiieo noi ?o p-oaaa?iaeo ?yae?a.

-?ioaa?ae, caeeoie ?yaeo Oaeei?a, aneiioioe/ia ??ai?noue, ia??ai?noue
Eaaaaa-Eaiaeao, ?-oaaa?iaee ?yae.

-eioaa?aeia ooieoeee eiiieaeniiai ia?aiaiiiai”.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.01. — iaoaiaoe/aneee
aiaeec. Einoeooo iaoaiaoeee IAI Oe?aeiu, Eeaa 1998.

, io /anoiuo noii eo ?-oaaa?iauo ?yaeia.

-eioaa?ae, inoaoie ?yaea Oaeei?a, aneiioioe/aneia ?aaainoai,
ia?aaainoai Eaaaaa-Eaiaeao, ?-oaaa?ia ?yae.

integrals of functions of complex variable”

The dissertation is devoted to the investigation of the rates
of the convergence

of the Taylor series and Faber series in uniform and integral metrics
on classes of

-integrals of functions, which are analytic in the disk D and the
domain G

respectively. In this work the asymptotic equates for upper bounds of
remainders of

, and analog of the Lebesque-

Landau inequality are established. Estimates of deviations of functions
from the

, from their partial p-Faber sums are obtained.

-integral, remainder of the Taylor series, asymptotic

equates,inequality of Lebesque- Landau, p-Faber series.

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