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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A random $ L\sp{1}$ function with divergent Walsh series


Author: Benjamin B. Wells
Journal: Proc. Amer. Math. Soc. 24 (1970), 794-796
MSC: Primary 42.16
MathSciNet review: 0261255
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Abstract: The purpose of this paper is to point out that the techniques of J. P. Kahane to arrive at almost everywhere divergent Fourier series may be carried over to the Fourier-Walsh system. In particular we construct a random $ {L^1}$ function whose Fourier-Walsh series almost surely (a. s.) diverges almost everywhere.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0261255-0
Keywords: Fourier-Walsh series, random function, almost surely divergent series
Article copyright: © Copyright 1970 American Mathematical Society