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Mat. Zametki, 2002, Volume 72, Issue 4, Pages 490–501 (Mi mz438)  

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

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 $\vec M=(M_1,…,M_n)$, 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 $\lambda >1$.

DOI: https://doi.org/10.4213/mzm438

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English version:
Mathematical Notes, 2002, 72:4, 454–465

Bibliographic databases:

UDC: 517.518
Received: 16.10.2001

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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\paper $\lambda$-Divergence of the Fourier Series of Continuous Functions of Several Variables
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\yr 2002
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. Yu. Antonov, “O raskhodimosti pochti vsyudu ryadov Fure nepreryvnykh funktsii dvukh peremennykh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(2) (2014), 497–505  mathnet
    2. Nikolai Yu. Antonov, “On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series”, Ural Math. J., 3:2 (2017), 14–21  mathnet  crossref  mathscinet
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