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

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

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English version:
Mathematical Notes, 2009, 86:5, 716–728

Bibliographic databases:

UDC: 517.52
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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• 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
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