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Matematicheskie Zametki, 2011, Volume 90, Issue 1, Pages 45–52
DOI: https://doi.org/10.4213/mzm8741 (Mi mzm8741) 		 
An Example of the Sequence of Coefficients of a Double Trigonometric Series

M. I. Dyachenko

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm8741
Abstract: We construct an example of a double sequence $a$ of nonnegative numbers that are monotone decreasing to zero in the first index for any fixed value of the second index and two Hadamard lacunary sequences of natural numbers such that the double trigonometric lacunary monotone series with the coefficients $a$ constructed from the first lacunary sequence is square-divergent almost everywhere and the one constructed from the second lacunary sequence is square-convergent almost everywhere.
Keywords: double trigonometric series, Hadamard lacunary sequence, square-convergent series, lacunary monotone coefficient, Pringsheim convergence, Fourier series.
Received: 12.03.2010
English version:
Mathematical Notes, 2011, Volume 90, Issue 1, Pages 41–47
DOI: https://doi.org/10.1134/S0001434611070066
Bibliographic databases:
Document Type: Article
UDC: 517.52
Language: Russian
Citation: M. I. Dyachenko, “An Example of the Sequence of Coefficients of a Double Trigonometric Series”, Mat. Zametki, 90:1 (2011), 45–52; Math. Notes, 90:1 (2011), 41–47
Citation in format AMSBIB
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