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Mat. Sb., 2018, Volume 209, Number 3, Pages 138–149 (Mi msb8881)  

This article is cited in 1 scientific paper (total in 1 paper)

Exact errors of best approximation for complex-valued periodic functions

M. I. Ganzburg

Department of Mathematics, Hampton University, Hampton, VA, USA

Abstract: We extend Nagy's theorem on best approximation by trigonometric polynomials in the $L_1$ metric to certain complex-valued periodic functions. We use this result to find exact constants of best approximation in $L_1$ and $L_\infty$ on some complex convolution classes. For classes of real-valued convolutions these constants were found by Nikol'skii. As an example, we apply these results to the Schwarz kernel and to the corresponding convolution classes.
Bibliography: 20 titles.

Keywords: trigonometric polynomial, complex-valued function, best approximation, Nagy's theorem, convolution classes.

DOI: https://doi.org/10.4213/sm8881

Full text: PDF file (756 kB)
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English version:
Sbornik: Mathematics, 2018, 209:3, 421–431

Bibliographic databases:

Document Type: Article
UDC: 517.538.5
MSC: 41A44, 41A10
Received: 13.12.2016 and 14.04.2017

Citation: M. I. Ganzburg, “Exact errors of best approximation for complex-valued periodic functions”, Mat. Sb., 209:3 (2018), 138–149; Sb. Math., 209:3 (2018), 421–431

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb8881
  • https://doi.org/10.4213/sm8881
  • http://mi.mathnet.ru/eng/msb/v209/i3/p138

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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. I. M. Ganzburg, “Exact errors of best approximation for complex-valued nonperiodic functions”, J. Approx. Theory, 229 (2018), 1–12  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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