Standard

Classes Of Convolutions With A Singular Family Of Kernels : Sharp Constants For Approximation By Spaces Of Shifts. / Vinogradov, O. L.

в: St. Petersburg Mathematical Journal, Том 32, № 2, 01.2021, стр. 233-260.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Vinogradov, OL 2021, 'Classes Of Convolutions With A Singular Family Of Kernels: Sharp Constants For Approximation By Spaces Of Shifts', St. Petersburg Mathematical Journal, Том. 32, № 2, стр. 233-260. https://doi.org/10.1090/spmj/1646

APA

Vinogradov, O. L. (2021). Classes Of Convolutions With A Singular Family Of Kernels: Sharp Constants For Approximation By Spaces Of Shifts. St. Petersburg Mathematical Journal, 32(2), 233-260. https://doi.org/10.1090/spmj/1646

Vancouver

Vinogradov OL. Classes Of Convolutions With A Singular Family Of Kernels: Sharp Constants For Approximation By Spaces Of Shifts. St. Petersburg Mathematical Journal. 2021 Янв.;32(2):233-260. https://doi.org/10.1090/spmj/1646

Author

Vinogradov, O. L. / Classes Of Convolutions With A Singular Family Of Kernels : Sharp Constants For Approximation By Spaces Of Shifts. в: St. Petersburg Mathematical Journal. 2021 ; Том 32, № 2. стр. 233-260.

BibTeX

@article{527e4d183e1c4f5e9f6e4bc7fc45838a,
title = "Classes Of Convolutions With A Singular Family Of Kernels: Sharp Constants For Approximation By Spaces Of Shifts",
abstract = "Let σ > 0, and let (Formula Presented). The paper is devoted to approximation of classes of functions f for every ε > 0 representable as (Formula Presented) where Fε is an entire function of type not exceeding ε, (Formula Presented), and (Formula Presented) The approximating space SB consists of functions of the form (Formula Presented). Under some conditions on G = {Gε} and B, linear operators Xσ,G,B with values in SB are constructed for which (Formula Presented) the constant Kσ,G (it is an analog of the well-known Favard constant) cannot be reduced, even if one replaces the left-hand side by the best approximation by the space SB. The results of the paper generalize classical inequalities for approximations by entire functions of exponential type and by splines.",
keywords = "Akhiezer–Kre˘ın–Favard type inequalities, convolution, sharp constants, Spaces of shifts",
author = "Vinogradov, {O. L.}",
note = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society",
year = "2021",
month = jan,
doi = "10.1090/spmj/1646",
language = "English",
volume = "32",
pages = "233--260",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - Classes Of Convolutions With A Singular Family Of Kernels

T2 - Sharp Constants For Approximation By Spaces Of Shifts

AU - Vinogradov, O. L.

N1 - Publisher Copyright: © 2021 American Mathematical Society

PY - 2021/1

Y1 - 2021/1

N2 - Let σ > 0, and let (Formula Presented). The paper is devoted to approximation of classes of functions f for every ε > 0 representable as (Formula Presented) where Fε is an entire function of type not exceeding ε, (Formula Presented), and (Formula Presented) The approximating space SB consists of functions of the form (Formula Presented). Under some conditions on G = {Gε} and B, linear operators Xσ,G,B with values in SB are constructed for which (Formula Presented) the constant Kσ,G (it is an analog of the well-known Favard constant) cannot be reduced, even if one replaces the left-hand side by the best approximation by the space SB. The results of the paper generalize classical inequalities for approximations by entire functions of exponential type and by splines.

AB - Let σ > 0, and let (Formula Presented). The paper is devoted to approximation of classes of functions f for every ε > 0 representable as (Formula Presented) where Fε is an entire function of type not exceeding ε, (Formula Presented), and (Formula Presented) The approximating space SB consists of functions of the form (Formula Presented). Under some conditions on G = {Gε} and B, linear operators Xσ,G,B with values in SB are constructed for which (Formula Presented) the constant Kσ,G (it is an analog of the well-known Favard constant) cannot be reduced, even if one replaces the left-hand side by the best approximation by the space SB. The results of the paper generalize classical inequalities for approximations by entire functions of exponential type and by splines.

KW - Akhiezer–Kre˘ın–Favard type inequalities

KW - convolution

KW - sharp constants

KW - Spaces of shifts

UR - http://www.scopus.com/inward/record.url?scp=85102835186&partnerID=8YFLogxK

U2 - 10.1090/spmj/1646

DO - 10.1090/spmj/1646

M3 - Article

AN - SCOPUS:85102835186

VL - 32

SP - 233

EP - 260

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 101356512