Arithmetic Means of Fourier Coefficients
Arithmetic Means of Fourier Coefficients
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.Introduction.Let 2^=1a"cos nx and 2^=16" …