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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 761–775 (Mi mz6613)  

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

On the Uniqueness and Integrability of Multiple Trigonometric Series

A. A. Talalyan

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: Under minimal constraints on the coefficients, we prove uniqueness theorems for multiple trigonometric series in which, instead of pointwise convergence, we consider the convergence of integral means of spherical, cubic, and other partial sums. We also obtain sufficient conditions for the integrability of multiple trigonometric series, i.e., conditions under which these series are Fourier series.

Keywords: multiple trigonometric series, Fourier series, integral means, spherical and cubic partial sums, periodic function, binary net of cubes, set of the second category

DOI: https://doi.org/10.4213/mzm6613

Full text: PDF file (539 kB)
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English version:
Mathematical Notes, 2009, 86:5, 716–728

Bibliographic databases:

UDC: 517.52
Received: 14.01.2009
Revised: 18.04.2009

Citation: A. A. Talalyan, “On the Uniqueness and Integrability of Multiple Trigonometric Series”, Mat. Zametki, 86:5 (2009), 761–775; Math. Notes, 86:5 (2009), 716–728

Citation in format AMSBIB
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\by A.~A.~Talalyan
\paper On the Uniqueness and Integrability of Multiple Trigonometric Series
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\vol 86
\issue 5
\pages 761--775
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\jour Math. Notes
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\vol 86
\issue 5
\pages 716--728
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  • http://mi.mathnet.ru/eng/mz6613
  • https://doi.org/10.4213/mzm6613
  • http://mi.mathnet.ru/eng/mz/v86/i5/p761

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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. A. A. Talalyan, “Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series”, Math. Notes, 88:1 (2010), 79–96  mathnet  crossref  crossref  mathscinet  isi
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