Compact sets of divergence for continuous functions on a Vilenkin group
HTML articles powered by AMS MathViewer
- by David C. Harris
- Proc. Amer. Math. Soc. 98 (1986), 436-440
- DOI: https://doi.org/10.1090/S0002-9939-1986-0857936-X
- PDF | Request permission
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
- John Gosselin, Almost everywhere convergence of Vilenkin-Fourier series, Trans. Amer. Math. Soc. 185 (1973), 345–370 (1974). MR 352883, DOI 10.1090/S0002-9947-1973-0352883-X
- Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992
- N. Ja. Vilenkin, On a class of complete orthonormal systems, Amer. Math. Soc. Transl. (2) 28 (1963), 1–35. MR 0154042, DOI 10.1090/trans2/028/01
- William R. Wade, Recent developments in the theory of Walsh series, Internat. J. Math. Math. Sci. 5 (1982), no. 4, 625–673. MR 679409, DOI 10.1155/S0161171282000611
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- 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