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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compact sets of divergence for continuous functions on a Vilenkin group


Author: David C. Harris
Journal: Proc. Amer. Math. Soc. 98 (1986), 436-440
MSC: Primary 43A75; Secondary 22E30, 42C10
MathSciNet review: 857936
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Abstract: Let $ G$ be a Vilenkin group. Let $ E \subset G$ be closed with Haar measure zero. We show there is a continuous function whose Vilenkin-Fourier series diverges at every point in $ E$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857936-X
PII: S 0002-9939(1986)0857936-X
Keywords: Walsh functions, Vilenkin group, sets of divergence
Article copyright: © Copyright 1986 American Mathematical Society