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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
DOI: https://doi.org/10.1090/S0002-9939-1986-0857936-X
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$.


References [Enhancements On Off] (What's this?)

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  • [2] Y. Katznelson, An introduction to harmonic analysis, Dover, New York, 1976. MR 0422992 (54:10976)
  • [3] N. Ja. Vilenkin, On a class of complete orthogonal systems, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 363-400; English transl., Amer. Math. Soc. Transl. (2) 28 (1963), 1-35. MR 0154042 (27:4001)
  • [4] W. R. Wade, Recent developments in the theory of Walsh series, Internat. J. Math & Math Sci. 5 (1982), 625-673. MR 679409 (84d:42033)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0857936-X
Keywords: Walsh functions, Vilenkin group, sets of divergence
Article copyright: © Copyright 1986 American Mathematical Society

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