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Walsh-Fourier series with coefficients of generalized bounded variation

Part of: Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  09 April 2009

F. Móricz
F. Móricz
Affiliation:
Bolyai Institute University of SzegedAradi Vertanuk Tere 1 6720 Szeged, Hungary
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Abstract

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We extend in different ways the class of null sequences of real numbers that are of bounded variation and study the Walsh-Fourier series of integrable functions on the interval [(0, 1) with such coefficients. We prove almost everywhere convergence as well as convergence in the pseu dometric of Lr(0, 1) for 0 < r < 1.

Keywords

Walsh-Paley systemcoefficient sequence of bounded variationpointwise convergenceconvergence in Lr(0, 1)-metric, 0 < r < 1arithmetic meande la Vallée Poussin meanDirichlet kernelFejér kernel.

MSC classification

Secondary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 458 - 465
Copyright
Copyright © Australian Mathematical Society 1989

References

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