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Апроксимація функцій дискретного аргументу: Автореф. дис… канд. фіз.- мат. наук / Ю.В. Великіна, НАН України. Ін-т математики. — К., 1999. — 15 с. —

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

?INOEOOO IAOAIAOEEE

AAEEE?IA THe?y Aaea???aia

OAeE 517.5

AI?IENEIAOe?ss OOIEOe?E AeENE?AOIIAI A?AOIAIOO

01.01.01 – iaoaiaoe/iee aiae?c

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a — 1999

Aeena?oaoe??th ? ?oeiien

?iaioo aeeiiaii ia eaoaae?? iaoaiaoe/iiai aiae?co
Aei?i?iiao?ianueeiai aea?aeaaiiai oi?aa?neoaoo

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

AAAAIEI Aeaaeeneaa
Oaaei?iae/,

eaoaae?a iaoaiaoe/iiai aiae?co Aei?i?iiao?ianueeiai aea?aeaaiiai
oi?aa?neoaoo, caa?aeoth/ee

Io?oe?ei? iiiiaioe – aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

EEAOI Aiaoie?e
Ieaenaiae?iae/,

Aei?i?iaeca?aeeinueeee aea?aeaaiee
oaoi?/iee oi?aa?neoao,

eaoaae?a i?eeeaaeii? iaoaiaoeee;

— eaiaeeaeao o?ceei-iaoaiaoe/ieo
iaoe,

IACA?AIEI Ieeiea Ieaen?eiae/,

noa?oee iaoeiaee ni?a?ia?oiee

?inoeoooo iaoaiaoeee IAI Oe?a?ie.

I?ia?aeia onoaiiaa: Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie

“Ee?anueeee iie?oaoi?/iee
?inoeooo”

Caoeno a?aeaoaeaoueny “ 01 ” ___/a?aiy____ 1999 ?ieo i _15___
aiae. 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, i.Ee?a-4, INI, aoe. Oa?auaie?anueea, 3, ?inoeooo iaoaiaoeee
IAI Oe?a?ie

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

Aaoi?aoa?ao ?ic?neaiee “__27__” ____ea?oiy_______ 1999 ?ieo

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
Ia?aaa?c?a N.A.

aeieoi? o?ceei-iaoaiaoe/ieo iaoe

5

1

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Ia?aaaaeia a?eueo?noue ieoaiue eeane/ii? oai??? ai?ieneiaoe??
noino?oueny aeine?aeaeaiue ooieoe?e oa ?o ocaaaeueiaiue c
eiioeioaeueieie iaeanoyie aecia/aiiy.

A oie aea /an a inoaii? ?iee a?aeaoaa?oueny aeineoue
aeoeaia aeei?enoaiiy oai?aoe/ieo ?acoeueoao?a oai???
ai?ieneiaoe?? a i?eeeaaeieo caaea/ao. Iniaeeai aeooaeueiei oea
noaei c iioe?aiiyi eiii’thoa?ii? oaoi?ee.

A?aeiii, ui oa?aeoa?ia iniaeea?noue ia/enethaaeueii?
oaoi?ee iieyaa? a oiio, ui aiia iia?o? aaee/eiaie, a?aoiaio
yeeo ci?ith?oueny ia iaia?a?aii, a aeene?aoii.

? ooo ne?ae cacia/eoe, ui, ye aeyaeeinue, aeene?aoecaoe?y
ooieoe?e iaia?a?aiiai a?aoiaioo, oiaoi caoaeaiiy ?o iaeano? aecia/aiiy
ia iiiaeeio oe?eeo /enae (oi/i?oa ia ??aiii??io ia?aaeo oi/ie), o
a?eueoino? aeiaaee?a ia i?eaeaoia aei canoinoaaiiy. Oae, iai?eeeaae,
aeene?aoecaoe?y nieaeia iaia?a?aiiai a?aoiaioo ia ? aeene?aoiei
nieaeiii, a noaiiaeoue niaith aeene?aoio ooieoe?th, yea iiai?noth
iicaaaeaia an?o aeno?aiaeueieo aeanoeainoae iaia?a?aiiai nieaeia ?,
aiane?aeie oeueiai, aea? cia/ii a?eueo? iioeaee ai?ieneiaoe?? a
ii??aiyii? c i?e?iaeiei aeene?aoiei nieaeiii.

A ca’yceo c oeei aeieeea iaiao?aei?noue a iiaoaeoaaii?
a?aeiia?aeii? oai?aoe/ii? aace aeey aeine?aeaeaiiy i?iaeai ai?ieneiaoe??
ooieoe?e aeene?aoiiai a?aoiaioo ?, cie?aia, aeey oi/iiai ?ica’yceo
aeno?aiaeueieo caaea/ oai??? ai?ieneiaoe??.

Iacaaaeath/e ia oa, ui ia?oa ?iaioa ii aeene?aoi?e
ai?ieneiaoe?? c’yaeeanue ua o 1919 ?ioe?, aea N.Aaeea-Ionnai
?icaeyioa aeene?aoio caaea/o iaee?auiai iaaeeaeaiiy ooieoe?e

aeaaa?a?/ieie iie?iiiaie ? ?ic?iaea aeai?eoi iiaoaeoaaiiy
iie?iiia iaee?aui? ai?ieneiaoe??, aeiiaaeaaia aoee eeoa iiiaeeiie?
?iaioe a oeueiio iai?yieo. Na?aae ieo a?aei?oeii ?iaioe
?.ss.?aiaca, A.O.?oa?iooaeia, I.Ae.Eaeaoi?eiaa ? ?.?.Aoa?iaia. A
aeaye?e i??? ieoaiiy aeene?aoii? ai?ieneiaoe?? ii?ooai? a
iiiia?ao?yo N. Ea?e?ia, Aeae. oii Iaeiaia ? I. Ii?aaiooa?ia,
A.I. Aeai’yiiaa ? A.I. Iaeacaiiaa.

Aeooaeuei?noue oaie. A inoaii? ?iee iai?oeeanue
aeoea?caoe?y aeine?aeaeaiue a aaeoc? aeene?aoii? ai?ieneiaoe??
Oea iieacaee, i?eiaeii?, ?iaioe A.I?ieona, E.Ai?a, A.O. Aaaaiea,
N.I. I?/oaiaa ? A.I.Eioaiiaa, E.Ooiaeea?a ? I.Iaiaana?yia,
?.Aeaea, C.Ae?ooe?aia, O.Eaia?a ? A.Niaeeiaia, I.Eaiiaa ?
A.Caooea. Cie?aia, a ?iaioao E. Ooiaeea?a ? I.Iaiaana?yia
aia?oa aoei aecia/aii aeene?aoi? nieaeie ? cai?iiiiiaaii
?o aeei?enoaiiy a caaea/ao iaoaiaoe/iiai i?ia?aioaaiiy oa a
caaea/ao iioeiaeueiiai ia/eneaiiy noi c aaeeeei /eneii
aeiaeaie?a.

?acii c oei, ne?ae cacia/eoe, ui aeiiaaeaaia
caeeoaeenue iaae??oaieie, ca aeiyoeii ie?aieo aeiaaee?a,
oae? caaea/? aeene?aoii? ai?ieneiaoe??, ye ia/eneaiiy oi/ieo
cia/aiue iioeaee ai?ieneiaoe?? aeene?aoieie nieaeiaie ia
iiiaeeiao iine?aeiaiinoae c iaiaaeaiith ??cieoeath caaeaiiai ii?yaeeo
a ??cieo i?inoi?ao, oi/ia ia/eneaiiy iiia?a/iee?a aeacaieo
iiiaeei, iioeiaeueia a?aeiiaeaiiy ? iiaoaeoaaiiy iioeiaeueieo
aeai?eoi?a a?aeiiaeaiiy cia/aiue e?i?eieo ooieoe?iiae?a. A a
caaea/? ciaoiaeaeaiiy oi/ii? eiinoaioe a aeene?aoieo ia??aiinoyo
oeio Eieiiai?iaa a ??aiii??i?e iao?eoe? i?ioyaii inoaii?o
?ie?a aoee c?iaeai? eeoa ia?o? e?iee.

Aeine?aeaeaiiy aeaii? aeena?oaoe?? naia ? i?enay/ai?
?ica’ycaiith aeuaaeacaieo caaea/.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.
Aeena?oaoe?y aeeiiaia a ?aieao aea?aeathaeaeaoii? oaie ? 122-95
“Aeno?aiaeuei? caaea/? ai?ieneiaoe?? oa ?o canoinoaaiiy aei
iioei?caoe?? aeai?eoi?a”, yea i?iaiaeeoueny ia eaoaae??
iaoaiaoe/iiai aiae?co Aei?i?iiao?ianueeiai aea?aeaaiiai
oi?aa?neoaoo.

Iaoa ? caaea/? aeine?aeaeaiue. Ciaeoe oi/i? cia/aiiy
iioeaee ai?ieneiaoe?? ?ioa?iieyoe?eieie ? iaee?aueie aeene?aoieie
nieaeiaie ye ie?aieo iine?aeiaiinoae, oae ? iiiaeei
iine?aeiaiinoae c iaiaaeaiith ??cieoeath aoaeue-yeiai ii?yaeeo a
??cieo i?inoi?ao.

Oi/ii ia/eneeoe iiia?a/ieee aeacaieo iiiaeei
iine?aeiaiinoae.

Ciaeoe oi/i? iioeaee iioeiaeueiiai a?aeiiaeaiiy ?
iiaoaeoaaoe iioeiaeuei? aeai?eoie a?aeiiaeaiiy cia/aiue e?i?eieo
ooieoe?iiae?a.

?ica’ycaoe caaea/o ciaoiaeaeaiiy oi/ii? eiinoaioe a
aeene?aoieo ia??aiinoyo oeio Eieiiai?iaa.

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

1. Io?eiai? oi/i? cia/aiiy iaciaiooaaieo eiinoaio a aeayeeo
aeene?aoieo ia??aiinoyo oeio Eieiiai?iaa.

2. Ia/eneai? oi/i? cia/aiiy eieiiai?ianueeeo ? e?i?eieo
iiia?a/iee?a aeia?eueii? ia?iino? iiiaeei iine?aeiaiinoae c
iaiaaeaiith ??cieoeath aoaeue-yeiai ii?yaeeo.

3. Ciaeaeaii oi/ia cia/aiiy iioeaee iioeiaeueiiai a?aeiiaeaiiy
cia/aiue e?i?eieo ooieoe?iiae?a ia aeuaaeacaieo iiiaeeiao ? iiaoaeiaaii
iioeiaeuei? aeai?eoie a?aeiiaeaiiy.

4. Ia/eneai? oi/i? cia/aiiy iioeaee ai?ieneiaoe?? ?ioa?iieyoe?eieie
? iaee?aueie aeene?aoieie nieaeiaie ye ?iaeea?aeoaeueieo
iine?aeiaiinoae, oae ? iiiaeei iine?aeiaiinoae.

Oe? ?acoeueoaoe, ia a?aei?io a?ae a?eueoino? a?aeiieo, aeathoue
inoaoi/iee ?ica’ycie aeuaaeacaieo caaea/.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?acoeueoaoe,
io?eiai? a aeena?oaoe??, a oaeiae iaoiaee ?o aeiaaaeaiiy
iiaeooue ciaeoe canoinoaaiiy a iiaeaeueoeo aeine?aeaeaiiyo
aeno?aiaeueieo caaea/ oai??? iaaeeaeaiiy ? oai??? iioeiaeueieo
aeai?eoi?a. Ii?yae c oai?aoe/iei, aiie iathoue ? i?aeoe/ia
cia/aiiy. An? io?eiai? ?acoeueoaoe aeiaaaeai? aei eiie?aoieo
ia/enethaaeueieo oi?ioe, ui aea? iiaeeea?noue ?o aaciina?aaeiueiai
aeei?enoaiiy a ia/enethaaeueieo caaea/ao oa i?ia?aioaaii?.

Iniaenoee aianie caeiaoaa/a. ?ocoeueoaoe ?icae?e?a 1, 2, 3, 4
? i?ae?icae?e?a 5.2 ? 5.3 io?eiai? naiino?eii, a ?acoeueoaoe
i?ae?icae?eo 5.1 — o ni?aaaoi?noa? c Aaeee?iei A.E.

Ai?iaaoe?y ?iaioe. ?acoeueoaoe, io?eiai? a aeena?oaoe??,
aeiiia?aeaeenue ia iaoeiaiio nai?ia?? eaoaae? oai??? ooieoe?e ?
iaoaiaoe/iiai aiae?co Aei?i?iiao?ianueeiai aea?aeaaiiai oi?aa?neoaoo,
iaoeiaiio nai?ia?? ii oai??? ai?ieneiaoe?? oi?aa?neoaoo ooaoo A?neiin?i,
i.Iaae?nii, NOA; ia ?icoe?aiiio iaoeiaiio nai?ia?? ?inoeoooo
iaoaiaoeee IAI Oe?a?ie; ia i?aeia?iaei?e eiioa?aioe?? 1993 ?ieo c
“Oai??? iaaeeaeaiue ? caaea/ ia/enethaaeueii? iaoaiaoeee”; a ?? oeie?
“?yaee Oo?’?: oai??y ? canoinoaaiiy” ?inoeoooo iaoaiaoeee IAI
Oe?a?ie.

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a
i’yoe ?iaioao, nienie yeeo iaaaaeaii a e?ioe? ?aoa?aoo.

No?oeoo?a ? ianya aeena?oaoe??. ?iaioa neeaaea?oueny ?c
anooio, i’yoe ?icae?e?a, aeniiae?a ? nieneo e?oa?aoo?e ?c 43
iaeiaioaaiue. Caaaeueiee ianya ?iaioe 113 noi??iie.

Aaoi? aeneiaeth? ue?o iiaeyeo nai?io iaoeiaiio ea??aieeia?
Aaaaiei A.O. ca iino?eio oaaao aei oe??? ?iaioe ? aeoaea
ei?eni? iaaiai?aiiy ??cieo ieoaiue, iia’ycaieo c oaiaoeeith
aeena?oaoe??.

INIIAIEE CI?NO ?IAIOE

Ia?oee ?icae?e aeena?oaoe?? iineoue anooiiee oa?aeoa?. A
iueiio aaaaeaii i?oiaiiaeueiee aacen i?inoi?o wmetafile8?
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??0e$???0e*???u@th??????Anoaiiaeaii ia/enethaaeueio oi?ioeo
aeey cia/aiue eii?aeeiao aoaeue-yei? iine?aeiaiino? wmetafile8?
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y??????Iaaaaeaii aeae?eueea icia/aiue aeene?aoieo nieaei?a ? aeiaaaeaii
?o aea?aaeaioi?noue i?ea?iaeueiiio icia/aiith. C oeeo icia/aiue
iaaaaeaii ooo iaeia (aeayeith i??ith, a?eueo oe?eaaa):
aeene?aoiee nieaei s ii?yaeeo m c aoceaie nk Z — oea
iine?aeiai?noue eiao?oe??io?a s(i ) = s a ?iceeaaeaii?

wmetafile8? ?????????????
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?MathType??P????u1/4y???? Io?eiaii cia?aaeaiiy aeene?aoieo
nieaei?a /a?ac aeene?aoi? yae?a Aa?ioee?.

O ae?oaiio ?icae?e? aeena?oaoe?? aeiaaaeaii iniiai? aeanoeaino?
aeene?aoieo nieaei?a ? aea/aii iiaeeea?noue ?ioa?iieyoe?? aeene?aoieie
nieaeiaie iaia?iiai ii?yaeeo c aoaeue-yeeie aoceaie, a oaeiae
aeene?aoieie nieaeiaie aeia?eueiiai ii?yaeeo c ??aiia?aeaeaeaieie
aoceaie i?aeoe/ii c aoaeue-yeeie oi/eaie ?ioa?iieyoe??. Aaaaeaii
aeene?aoi? aiaeiae aeea?iaeo nieaei?a wmetafile8? ??U????????????
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wmetafile8? ??E???????????
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ioe?a oa aeno?aiaeueieo cia/aiue oaeeo nieaei?a ? io?eiaii
ia/enethaaeuei? oi?ioee aeey ?o ii?i. Aeei?enoaiiy aeene?aoieo aeea?iaeo
nieaei?a oa ?o iiaeeo?eaoe?e

aeicaieeei aaoi?o aeaoe a 1998 ?ioe? ?ica’ycie iaei??? aeno?aiaeueii?
caaea/? – ciaoiaeaeaiiy oi/ii? eiinoaioe a aeene?aoi?e ia??aiino? oeio
Eieiiai?iaa a i?inoi?? wmetafile8? ??????????????
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?icae?eo ? ianooii? oai?aie.

Oai?aia 3.1.2. Iaoae wmetafile8? ??O????????????
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Oai?aia 3.2.1 Aeey iine?aeiaiino? wmetafile8? ??O????????????
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oeeo ?acoeueoao?a, ? iiaee ? oe?eeii a?ae??ciy?oueny a?ae a?aeiieo
iaoiae?a, ye? aoee canoiniaai? ?ai?oa ?ioeie aaoi?aie ye o iaia?a?aiiio
oae ? a aeene?aoiiio aeiaaeeao.

Iaaaaeai? ?acoeueoaoe neeaaeathoue ci?no o?aoueiai
?icae?eo aeena?oaoe??.

A /aoaa?oiio ?icae?e? aeena?oaoe?? ciaeaeaii oi/ia cia/aiiy
iioeaee

ai?ieneiaoe?? ?ioa?iieyoe?eieie aeene?aoieie nieaeiaie a oi/oe? ? a
ii?i? wmetafile8? ???????????????
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4.1.1. Aeey aoaeue-yei? iine?aeiaiino? wmetafile8?
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oeeo aea iiiaeei io?eiaii oi/ia cia/aiiy iaee?aui? ai?ieneiaoe??
aeene?aoieie nieaeiaie a i?inoi?ao wmetafile8? ???????????????
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wmetafile8? ?????????????
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iaee?aui? ai?ieneiaoe?? aeene?aoieie o?eaiiiiao?e/ieie iie?iiiaie
ia iiiaeeiao wmetafile8? ??I????????????
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Oai?aia 4.3.5.

sseui wmetafile8? ??u????????????
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Oai?aia 4.4.5. Aeey aoaeue-yeeo wmetafile8? ???????????????
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aeiaaaeaii? ?acoeueoao?a oeueiai ?icae?eo aeei?enoiaothoueny
?aea? io?eiaiiy a?aeiia?aeieo ?acoeueoao?a o iaia?a?aiiio
aeiaaeeo, aea aeene?aoia niaoeeo?ea ?icaeyiooeo caaea/ iio?aaoaaea
nai???aeieo i?ea?iaeueieo oaoi?/ieo cania?a.

A i’yoiio ?icae?e? ae??oaia caaea/a i?i oi/ia cia/aiiy
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iaoo?aeueieo wmetafile8? ?? wmetafile8?
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cia/aiiy iioeaee iioeiaeueiiai a?aeiiaeaiiy cia/aiue aeia?eueieo
e?i?eieo ooieoe?iiae?a c aeei?enoaiiyi aeia?eueii? ?ioi?iaoe??.
Aeey ?ioi?iaoe?e, ye? aeei?enoiaothoue ie?ai? eii?aeeiaoe
iine?aeiaiino?, ii?yae c oi/iei cia/aiiyi iioeaee iioeiaeueiiai
a?aeiiaeaiiy ia iiiaeei? wmetafile8? ??I????????????
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AENIIAEE

Iniiaieie ?acoeueoaoaie ?iaioe, ye? aeiinyoueny ia
caoeno, ?:

1. Oi/i? cia/aiiy iaciaiooaaieo eiinoaio a aeene?aoieo
ia??aiinoyo oeio Eieiiai?iaa c aeia?eueiei ii?yaeeii noa?oi?
??cieoe?.

2. Oi/i? cia/aiiy eieiiai?ianueeeo oa e?i?eieo iiia?a/iee?a
aeia?eueii? ia?iino? iiiaeei iine?aeiaiinoae c iaiaaeaiith
??cieoeath aoaeue-yeiai ii?yaeeo.

3. Oi/ia cia/aiiy iioeaee iioeiaeueiiai a?aeiiaeaiiy cia/aiue
e?i?eieo ooieoe?iiae?a ia iiiaeeiao iine?aeiaiinoae c iaiaaeaiith
??cieoeath aoaeue-yeiai ii?yaeeo ? iioeiaeuei? aeai?eoie
a?aeiiaeaiiy.

4. Oi/i? cia/aiiy ai?ieneiaoe?? ?ioa?iieyoe?eieie ? iaee?aueie
aeene?aoieie nieaeiaie ye ?iaeea?aeoaeueieo iine?aeiaiinoae, oae ?
iiiaeei iine?aeiaiinoae.

Iniiai? iieiaeaiiy aeena?oaoe?? iioae?eiaai? a ianooiieo ?iaioao

1. Velikina J.V. Sharp constants in discrete Kolmogorov – type
inequalities // East J. Approx. – 1999. – 5, 1. – S. 89 – 100.

2. Velikina J.V. Approximation of linear functionals of
finite-dimensional spaces by functionals defined on the spaces of
smaller dimensional // I?aoe? ?i-oo Iaoaiaoeee IAI Oe?a?ie. –
1998. – O.20. – N. 72-76.

3. Aaeeeeia TH.A., Aaeeeei A.E. Iiia?a/ieee iiiaeanoa ooieoeee
aeene?aoiiai a?aoiaioa // Oe?. iao. aeo?i. – 1996. – 48, ? 10. – N.
1311-1320.

4. Aaeeeeia TH.A. Iaeioi?ua ia?aaainoaa, naycuaathuea ii?iu
/eneiauo iineaaeiaaoaeueiinoae e eo ?aciinoae // Oai??y
iaaeeaeaiiy oa caaea/? ia/enethaaeueii? iaoaiaoeee: Oace aeii.
i?aeia?. eiio. –Aei?i?iiao?ianuee, 1993. – N. 40.

5. Aaeeeeia TH.A. Aeene?aoiua nieaeiu a iioeiaeueiie
aii?ieneiaoeee // ?? oeiea “?yaee Oo?’?: oai??y ? canoinoaaiiy”:
Oace aeii. – Ee?a, 1997. – N. 33.

Aaeee?ia TH.A. Ai?ieneiaoe?y ooieoe?e aeene?aoiiai a?aoiaioo.
— ?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 iaoaiaoeee IAI Oe?a?ie, Ee?a,
1999.

Aeena?oaoe?th i?enay/aii aeno?aiaeueiei caaea/ai aeene?aoii?
ai?ieneiaoe??. A aeena?oaoe?? aeaii iiaiee ?ica’ycie caaea/?
ciaoiaeaeaiiy oi/ii? eiinoaioe a ia??aiino? oeio Eieiiai?iaa aeey
ioe?iee a ??aiii??i?e iao?eoe? ii?ie ??cieoe? iine?aeiaiino?
/a?ac ii?io naii? iine?aeiaiino? oa ii?io ?? ??cieoe?
aoaeue-yeiai ii?yaeeo. Canoiniaaiee i?e oeueiio iaoiae
a?ae??ciy?oueny a?ae a?aeiieo iaoiae?a, ye? aoee aaeeo? ?ai?oa
ye o iaia?a?aiiio, oae ? a aeene?aoiiio aeiaaeeao. Ia/eneaii
eieiiai?ianuee? oa e?i?ei? iiia?a/ieee aoaeue-yeeo aei??iinoae
iiiaeei iine?aeiaiinoae c iaiaaeaiith ??cieoeath aeia?eueiiai
ii?yaeeo. Ae??oaii caaea/o iioeiaeueiiai a?aeiiaeaiiy e?i?eieo
ooieoe?iiae?a ia oaeeo iiiaeeiao. Anoaiiaeaii oi/i? cia/aiiy
iioeaee ai?ieneiaoe?? ?ioa?iieyoe?eieie oa iaee?aueie aeene?aoieie
nieaeiaie ia iiiaeeiao iine?aeiaiinoae c iaiaaeaiith a ??cieo
iao?eeao ??cieoeath aoaeue-yeiai ii?yaeeo.

Eeth/ia? neiaa : aeene?aoiee, nieaei, ai?ieneiaoe?y, ?ioa?iieyoe?y,
iiia?a/iee, a?aeiiaeaiiy.

Aaeeeeia TH.A. Aii?ieneiaoeey ooieoeee aeene?aoiiai
a?aoiaioa.–?oeiienue. 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,
1999.

Aeenna?oaoeey iinayuaia yeno?aiaeueiui caaea/ai aeene?aoiie
aii?ieneiaoeee. A aeenna?oaoeee aeaii iieiia ?aoaiea caaea/e
iaoiaeaeaiey oi/iie eiinoaiou a ia?aaainoaa oeia Eieiiai?iaa
aeey ioeaiee a ?aaiiia?iie iao?eea ii?iu ?aciinoe
iineaaeiaaoaeueiinoe /a?ac ii?io naiie iineaaeiaaoaeueiinoe e
ii?io a? ?aciinoe ethaiai ii?yaeea. I?eiaiaiiue i?e yoii iaoiae
ioee/aaony io ecaanoiuo iaoiaeia, eioi?ua auee eniieueciaaiu
?aiaa eae a iai?a?uaiii, oae e a aeene?aoiii neo/ayo. Au/eneaiu
eieiiai?ianeea e eeiaeiua iiia?a/ieee ethauo ?acia?iinoae
iiiaeanoa iineaaeiaaoaeueiinoae n ia?aie/aiiie ?aciinoueth
i?iecaieueiiai ii?yaeea. ?aoaia caaea/a iioeiaeueiiai
ainnoaiiaeaiey eeiaeiuo ooieoeeiiaeia ia oaeeo iiiaeanoaao. Aeey
eioi?iaoeee, eioi?ua eniieuecotho cia/aiey ioaeaeueiuo eii?aeeiao
iineaaeiaaoaeueiinoe, iaeaeaii oi/iia cia/aiea iia?aoiinoe, e iino?iai
iioeiaeueiue aeai?eoi ainnoaiiaeaiey. Iieo/aiu ioeaiee aeey iia?aoiinoe
i?eaeeaeaiey i?iecaieueiie iineaaeiaaoaeueiinoe eioa?iieyoeeiiiuie
aeene?aoiuie nieaeiaie e onoaiiaeaia iioeiaeueiay ii oi/iinoe
oi?ioea aeey i?eaeeaeaiiuo au/eneaiee eii?aeeiao
iineaaeiaaoaeueiinoae.

Ii?aaeaeaiu aeene?aoiua aiaeiae yaea? Aa?ioeee e n eo
iiiiuueth iieo/aiu au/eneeoaeueiua oi?ioeu aeey cia/aiee
eii?aeeiao i?iecaieueiie iineaaeiaaoaeueiinoe.

Aeai ?yae ii?aaeaeaiee aeene?aoiuo nieaeiia e aeieacaia eo
yeaeaaeaioiinoue, a /anoiinoe, i?e iiiiue A – nieaeiia onoaiiaeaia
naycue aeene?aoiuo nieaeiia n iai?a?uaiuie. Aaaaeaiu aeene?aoiua
aiaeiae yeea?iauo nieaeiia e eo iiaeeoeeaoeee. Enneaaeiaaiu eo
naienoaa e iieo/aiu au/eneeoaeueiua oi?ioeu aeey cia/aiee e ii?i
yoeo nieaeiia e eo ?aciinoae i?iecaieueiiai ii?yaeea.

Iaeaeaiu oi/iua cia/aiey i?eaeeaeaiey a i?ino?ainoaao
wmetafile8? ???????????????
???????????yyy????.????1?????????????
?????&??yyyy?????Ayyy?yyyA????????&??MathType??
Onoaiiaeaiu naienoaa iaaic?anoathueo ia?anoaiiaie
iineaaeiaaoaeueiinoae, ia iniiaaiee eioi?uo aeieacaia
yeno?aiaeueiinoue aeene?aoiuo aiaeiaia yeea?iauo nieaeiia a ii?ia
i?ino?ainoa wmetafile8? ???????????????
???????????yyy????.????1?????????????
?????&??yyyy?????Ayyy?yyyA????????&??MathType??
Iieo/aiu aeinoaoi/ii yooaeoeaiua e i?inoua a eniieueciaaiee
au/eneeoaeueiua oi?ioeu aeey aii?ieneiaoeee aeene?aoiuie nieaeiaie
ooieoeee eae aeene?aoiiai, oae e iai?a?uaiiai a?aoiaioa.

Eeth/aaua neiaa: aeene?aoiue, nieaei, aii?ieneiaoeey,
eioa?iieyoeey, iiia?a/iee, ainnoaiiaeaiea.

Velikina Yu.V. Approximation of functions of discrete argument.–
Manuscript. Thesis for the degree of the candidate of physical and
mathematical sciences, speciality 01.01.01 — mathematical analysis. —
Institute of Mathematics of the NAS of Ukraine, 1999.

The dissertation is dedicated to the solution of extremal problems
of discrete approximation. In the dissertation, we give complete
solution to the problem of finding sharp constants in the
Kolmogorov-type inequality estimating the norm of a difference of a
sequence via the norms of the sequence and its difference of any degree
in the uniform metric. The method used in the proof differs from the
known methods that were used earlier by different authors both in the
discrete and in the continuous cases. We compute Kolmogorov and
linear widths of any dimension of the sets of sequences with the
bounded difference of arbitrary order and solve the problem of optimal
recovery. We establish exact values of the error of interpolation and
best approximation by discrete splines on the sets of sequences with
the difference of any order bounded in different metrics.

Keywords: discrete, spline, approximation, interpolation,
width, recovery.

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