Standard

Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions. / Vinogradov, O. L.

In: Siberian Mathematical Journal, Vol. 58, No. 2, 01.03.2017, p. 190-204.

Research output: Contribution to journal › Article › peer-review

Harvard

Vinogradov, OL 2017, 'Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions', Siberian Mathematical Journal, vol. 58, no. 2, pp. 190-204. https://doi.org/10.1134/S0037446617020021

APA

Vinogradov, O. L. (2017). Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions. Siberian Mathematical Journal, 58(2), 190-204. https://doi.org/10.1134/S0037446617020021

Vancouver

Vinogradov OL. Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions. Siberian Mathematical Journal. 2017 Mar 1;58(2):190-204. https://doi.org/10.1134/S0037446617020021

Author

Vinogradov, O. L. / Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions. In: Siberian Mathematical Journal. 2017 ; Vol. 58, No. 2. pp. 190-204.

BibTeX

@article{ad785aa399ec4b9c9a93f8aff6c960a7,
title = "Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions",
abstract = "We establish sharp estimates for the best approximations of convolution classes by entire functions of exponential type. To obtain these estimates, we propose a new method for testing Nikol{\textquoteright}skiĭ-type conditions which is based on kernel periodization with an arbitrarily large period and ensuing passage to the limit. As particular cases, we obtain sharp estimates for approximation of convolution classes with variation diminishing kernels and generalized Bernoulli and Poisson kernels.",
keywords = "convolution, entire function of exponential type, inequalities of Akhiezer–Kreĭn–Favard type",
author = "Vinogradov, {O. L.}",
year = "2017",
month = mar,
day = "1",
doi = "10.1134/S0037446617020021",
language = "English",
volume = "58",
pages = "190--204",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions

AU - Vinogradov, O. L.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We establish sharp estimates for the best approximations of convolution classes by entire functions of exponential type. To obtain these estimates, we propose a new method for testing Nikol’skiĭ-type conditions which is based on kernel periodization with an arbitrarily large period and ensuing passage to the limit. As particular cases, we obtain sharp estimates for approximation of convolution classes with variation diminishing kernels and generalized Bernoulli and Poisson kernels.

AB - We establish sharp estimates for the best approximations of convolution classes by entire functions of exponential type. To obtain these estimates, we propose a new method for testing Nikol’skiĭ-type conditions which is based on kernel periodization with an arbitrarily large period and ensuing passage to the limit. As particular cases, we obtain sharp estimates for approximation of convolution classes with variation diminishing kernels and generalized Bernoulli and Poisson kernels.

KW - convolution

KW - entire function of exponential type

KW - inequalities of Akhiezer–Kreĭn–Favard type

UR - http://www.scopus.com/inward/record.url?scp=85018830343&partnerID=8YFLogxK

U2 - 10.1134/S0037446617020021

DO - 10.1134/S0037446617020021

M3 - Article

AN - SCOPUS:85018830343

VL - 58

SP - 190

EP - 204

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 15680199