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February 2001 Comments on the absolute convergence of Fourier series
László LEINDLER
Hokkaido Math. J. 30(1): 221-230 (February 2001). DOI: 10.14492/hokmj/1350911933

Abstract

We give sufficient conditions for the convergence of the series having the following form $$\sum_{k=1}^{\infty}k^{\delta}(\varphi(|a_{n_{k}}|)+\varphi(|b_{n_{k}}|)) ,$$ where $a_{k}$ and $b_{k}$ are Fourier coefficients, $\delta\geq 0$, $\varphi(u)(u\geq 0)$ is an increasing concave function, and $\{n_{k}\}$ is a certain increasing sequence of natural numbers.

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László LEINDLER. "Comments on the absolute convergence of Fourier series." Hokkaido Math. J. 30 (1) 221 - 230, February 2001. https://doi.org/10.14492/hokmj/1350911933

Information

Published: February 2001
First available in Project Euclid: 22 October 2012

zbMATH: 1002.42003
MathSciNet: MR1815890
Digital Object Identifier: 10.14492/hokmj/1350911933

Subjects:
Primary: 42A48
Secondary: 42A55

Rights: Copyright © 2001 Hokkaido University, Department of Mathematics

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Vol.30 • No. 1 • February 2001
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