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Matematicheskie Zametki, 2009, Volume 86, Issue 5, Pages 761–775
DOI: https://doi.org/10.4213/mzm6613 (Mi mzm6613) 		 
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
Full-text PDF (539 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm6613
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.
Received: 14.01.2009
Revised: 18.04.2009
English version:
Mathematical Notes, 2009, Volume 86, Issue 5, Pages 716–728
DOI: https://doi.org/10.1134/S0001434609110145
Bibliographic databases:
UDC: 517.52
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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