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

 

A growth condition for Fourier coefficients of functions of bounded entropy norm


Author: W. Christopher Lang
Journal: Proc. Amer. Math. Soc. 112 (1991), 433-439
MSC: Primary 42A16
MathSciNet review: 1045141
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Abstract: A simple growth condition is found for the Fourier coefficients of continuous $ 1$-periodic functions of bounded $ k$-entropy norm. This growth condition is equivalent to the condition given by Dabrowski. The entropy norms of certain random Fourier series are considered.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1045141-8
PII: S 0002-9939(1991)1045141-8
Keywords: Fourier coefficients, entropy norm, random Fourier series
Article copyright: © Copyright 1991 American Mathematical Society