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

$\lambda$-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

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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• http://mi.mathnet.ru/eng/mz438
• https://doi.org/10.4213/mzm438
• http://mi.mathnet.ru/eng/mz/v72/i4/p490

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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
2. Nikolai Yu. Antonov, “On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series”, Ural Math. J., 3:2 (2017), 14–21
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