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Smoothness conditions and integrability theorems on bounded Vilenkin groups

Part of: Abstract harmonic analysis Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Walter R. Bloom  and
John J. F. Fournier
Walter R. Bloom
Affiliation:
School of Mathematical and Physical SciencesMurdoch UniversityPerth, Western Australia 6150, Australia
John J. F. Fournier
Affiliation:
Department of MathematicsUniversity of British ColumbiaVancouver, CanadaV6T 1Y4
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Abstract

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Various criteria, in terms of forward differences and related operations on coefficients, are shown to imply that certain series on bounded Vilenkin groups represent integrable functions. These results include analogues of known integrability theorems for trigonometric series. The method of proof is to pass from the given series to a derived series, and to deduce the integrability of the original series from smoothness properties of the latter.

MSC classification

Secondary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 43A50: Convergence of Fourier series and of inverse transforms 43A70: Analysis on specific locally compact and other abelian groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 1 , August 1988 , pp. 46 - 61
Copyright
Copyright © Australian Mathematical Society 1988

References

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