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

Lang, W. Christopher

doi:10.1090/S0002-9939-1991-1045141-8

A growth condition for Fourier coefficients of functions of bounded entropy norm
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Proc. Amer. Math. Soc. 112 (1991), 433-439 Request permission

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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