Arithmetic means of Fourier coefficients

Sinha, Rajendra

doi:10.1090/S0002-9939-1976-0397274-9

Arithmetic means of Fourier coefficients
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Proc. Amer. Math. Soc. 55 (1976), 83-86 Request permission

Addendum: Proc. Amer. Math. Soc. 60 (1976), 243-244.

Abstract:

Given the Fourier coefficients of an even continuous function, we find a necessary and sufficient condition such that their arithmetic means are the Fourier coefficients of an odd continuous function. A similar result is shown for those Lipschitz classes whose elements are automatically equivalent to continuous functions.

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Notes on some points in the integral calculus

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