Optimal Recovery of a Function Holomorphic in a Polydisc from Its Approximate Values on a Part of the Skeleton

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Optimal Recovery of a Function Holomorphic in a Polydisc from Its Approximate Values on a Part of the Skeleton. / Akopyan, R.
в: Siberian Advances in Mathematics, Том 33, № 4, 2023, стр. 261-277.

Результаты исследований: Вклад в журнал › Статья › Рецензирование

BibTeX

@article{14ad8e68f3ec4962a75f473722304be6,

title = "Optimal Recovery of a Function Holomorphic in a Polydisc from Its Approximate Values on a Part of the Skeleton",

abstract = "We consider a series of related extremal problems for holomorphic functions in a polydisc (Formula presented.), (Formula presented.). The sharp inequality (Formula presented.), with (Formula presented.), is established between the value of a functionholomorphic in (Formula presented.) and the norms of its limit values onmeasurable sets (Formula presented.), where (Formula presented.) and (Formula presented.) is the skeleton (the Shilov boundary) of (Formula presented.). This result is an analog of the two-constanttheorem by the Nevanlinna brothers. We study conditions under which the above inequalityprovides us with the value of the modulus of continuity of the functional for holomorphic extensionof a function on (Formula presented.) at a prescribed point of the polydisc. In thesecases, a solution was obtained of the problem of optimal recovery of a function from approximatelygiven values on a part of the skeleton (Formula presented.) and the relatedproblem of the best approximation of the functional of the continuation of a function into apolydisk from (Formula presented.) {\textcopyright} 2023, Pleiades Publishing, Ltd.",

author = "R. Akopyan",

note = "The work was partially supported by the Russian Scientific Foundation (project no. 22-21-00526).",

year = "2023",

doi = "10.1134/S1055134423040016",

language = "English",

volume = "33",

pages = "261--277",

journal = "Siberian Advances in Mathematics",

issn = "1055-1344",

publisher = "Springer Verlag",

number = "4",

}

RIS

TY - JOUR

T1 - Optimal Recovery of a Function Holomorphic in a Polydisc from Its Approximate Values on a Part of the Skeleton

AU - Akopyan, R.

N1 - The work was partially supported by the Russian Scientific Foundation (project no. 22-21-00526).

PY - 2023

Y1 - 2023

N2 - We consider a series of related extremal problems for holomorphic functions in a polydisc (Formula presented.), (Formula presented.). The sharp inequality (Formula presented.), with (Formula presented.), is established between the value of a functionholomorphic in (Formula presented.) and the norms of its limit values onmeasurable sets (Formula presented.), where (Formula presented.) and (Formula presented.) is the skeleton (the Shilov boundary) of (Formula presented.). This result is an analog of the two-constanttheorem by the Nevanlinna brothers. We study conditions under which the above inequalityprovides us with the value of the modulus of continuity of the functional for holomorphic extensionof a function on (Formula presented.) at a prescribed point of the polydisc. In thesecases, a solution was obtained of the problem of optimal recovery of a function from approximatelygiven values on a part of the skeleton (Formula presented.) and the relatedproblem of the best approximation of the functional of the continuation of a function into apolydisk from (Formula presented.) © 2023, Pleiades Publishing, Ltd.

AB - We consider a series of related extremal problems for holomorphic functions in a polydisc (Formula presented.), (Formula presented.). The sharp inequality (Formula presented.), with (Formula presented.), is established between the value of a functionholomorphic in (Formula presented.) and the norms of its limit values onmeasurable sets (Formula presented.), where (Formula presented.) and (Formula presented.) is the skeleton (the Shilov boundary) of (Formula presented.). This result is an analog of the two-constanttheorem by the Nevanlinna brothers. We study conditions under which the above inequalityprovides us with the value of the modulus of continuity of the functional for holomorphic extensionof a function on (Formula presented.) at a prescribed point of the polydisc. In thesecases, a solution was obtained of the problem of optimal recovery of a function from approximatelygiven values on a part of the skeleton (Formula presented.) and the relatedproblem of the best approximation of the functional of the continuation of a function into apolydisk from (Formula presented.) © 2023, Pleiades Publishing, Ltd.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85179751044

U2 - 10.1134/S1055134423040016

DO - 10.1134/S1055134423040016

M3 - Article

VL - 33

SP - 261

EP - 277

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 4

ER -

ID: 49821418