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Multiple fourier integral and multiple fourier series under square summation
Siberian Mathematical Journal, 1990The author studies a correlation between the convergence of multiple Fourier series and corresponding multiple Fourier integral. For a \(2\pi\)- periodic function f(x), \(x\in R^ N\) with the Fourier decomposition \(\sum_{k}c_ ke^{ikx}\sim f(x),\) let us denote \[ S_ n(x;f)=\sum_{| k_ 1| \leq n_ 1}...\sum_{| k_ N| \leq n_ N}c_ ke^{i(k_ 1x_ 1+...+k_ Nx_
I L Bloshanskii
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On Bohr's theorem for multiple Fourier series
Mathematical Notes, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Remarks on multiple Fourier series
Analysis Mathematica, 1976Статья посвящена сле дующим вопросам: (1) абс трактные кратные ряды Фурье и связанные с ними инте рполяционные простр анства (характеризация инте рполяционных пространств, свойств а коэффициентов Фурь е, лакунарные ряды), (2) кра тные тригонометриче ские ряды (периодические п ространства Соболев а—Бесова, свойства коэффициен тов Фурье, характеризация ...
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Summation of multiple Fourier series in multiplicative systems
Mathematical Notes, 1986The author proves two theorems on the estimates of Lebesgue constants and formulates a result for the very strong summability following the first part of the paper.
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The rate ofu-convergence of multiple Fourier series
Acta Mathematica Hungarica, 1995The best possible estimates for the rate of \(u\)-convergence of multiple trigonometric Fourier series in \(L^p\)-metric are obtained.
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A note on multiple rational Fourier series
Periodica Mathematica Hungarica, 2021Some theorems are proved for multiple rational Fourier coefficients of functions from the Lip\((p;\alpha_1, \ldots, \alpha_N)\) class and functions having \(\Phi- \Lambda\)-bounded variation.
H. J. Khachar, R. G. Vyas
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On the absolute convergence of multiple fourier series
Acta Mathematica Hungarica, 2007Let \(f:\mathbb R^N\to \mathbb C\) be a periodic function with period \(2\pi\) in each variable. The authors obtain sufficient conditions for the absolute convergence of the multiple Fourier series of the function \(f\) in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative
Móricz, Ferenc, Veres, Antal
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Pick’s Theorem and Convergence of Multiple Fourier Series
The American Mathematical Monthly, 2021We add another brick to the large building comprising proofs of Pick’s theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick’s theorem and the po...
Brandolini, Luca +3 more
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Multiple fourier series and integrals
Journal of Soviet Mathematics, 1984Translation from Itogi Nauki Tekh., Ser. Mat. Anal. 19, 3-54 (Russian) (1982; Zbl 0511.42021).
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