Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] J. Gosselin, Almost everywhere convergence of Vilenkin-Fourier series, Trans. Amer. Math. Soc. 185 (1973), 345-370. MR 0352883 (50:5369)
  • [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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A75, 22E30, 42C10

Retrieve articles in all journals with MSC: 43A75, 22E30, 42C10

Additional Information

Keywords: Walsh functions, Vilenkin group, sets of divergence
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society