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Matematicheskie Zametki, 2002, Volume 72, Issue 4, Pages 490–501
DOI: https://doi.org/10.4213/mzm438
(Mi mzm438)
 

This article is cited in 2 scientific papers (total in 2 papers)

$\lambda$-Divergence of the Fourier Series of Continuous Functions of Several Variables

A. N. Bakhvalov

M. V. Lomonosov Moscow State University
Full-text PDF (232 kB) Citations (2)
References:
Abstract: In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called $\lambda$-convergent if the limit of rectangular partial sums over all indices $\vec M=(M_1,\dots ,M_n)$, for which $1/\lambda \le M_j/M_k\le \lambda $ for all $j$ and $k$ exists. In the space of arbitrary even dimension $2m$ we construct an example of a continuous function with an estimate of the modulus of continuity $\omega (F,\delta)=\underset {\delta \to +0}\to O(\ln ^{-m}(1/\delta))$ such that its Fourier series is $\lambda$-divergent everywhere for any $\lambda >1$.
Received: 16.10.2001
English version:
Mathematical Notes, 2002, Volume 72, Issue 4, Pages 454–465
DOI: https://doi.org/10.1023/A:1020524110083
Bibliographic databases:
UDC: 517.518
Language: Russian
Citation: A. N. Bakhvalov, “$\lambda$-Divergence of the Fourier Series of Continuous Functions of Several Variables”, Mat. Zametki, 72:4 (2002), 490–501; Math. Notes, 72:4 (2002), 454–465
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm438
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:47
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