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Sibirsk. Mat. Zh., 2017, Volume 58, Number 2, Pages 251–269 (Mi smj2857)  

This article is cited in 3 scientific papers (total in 3 papers)

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

O. L. Vinogradov

St. Petersburg State University, St. Petersburg, Russia

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'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: inequalities of Akhiezer–Kreĭn–Favard type, entire function of exponential type, convolution.

DOI: https://doi.org/10.17377/smzh.2017.58.202

Full text: PDF file (382 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:2, 190–204

Bibliographic databases:

UDC: 517.5
MSC: 35R30
Received: 08.04.2016

Citation: O. L. Vinogradov, “Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions”, Sibirsk. Mat. Zh., 58:2 (2017), 251–269; Siberian Math. J., 58:2 (2017), 190–204

Citation in format AMSBIB
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\paper Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 2
\pages 251--269
\mathnet{http://mi.mathnet.ru/smj2857}
\crossref{https://doi.org/10.17377/smzh.2017.58.202}
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\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 2
\pages 190--204
\crossref{https://doi.org/10.1134/S0037446617020021}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. L. Vinogradov, “Tochnye konstanty priblizhenii klassov svertok s summiruemym yadrom prostranstvami sdvigov”, Algebra i analiz, 30:5 (2018), 112–148  mathnet
    2. O. L. Vinogradov, “Average dimension of shift spaces”, Lobachevskii J. Math., 39:5 (2018), 717–721  crossref  mathscinet  zmath  isi  scopus
    3. L. P. Castro, L. T. Minh, N. M. Tuan, “New convolutions for quadratic-phase Fourier integral operators and their applications”, Mediterr. J. Math., 15:1 (2018), 13  crossref  mathscinet  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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