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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
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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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Linking options:
http://mi.mathnet.ru/eng/mz6613https://doi.org/10.4213/mzm6613 http://mi.mathnet.ru/eng/mz/v86/i5/p761
Citing articles on Google Scholar:
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Related articles on Google Scholar:
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English articles
This publication is cited in the following articles:
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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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