Vol. 80, No. 1, 1979

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Fourier series with bounded convolution powers

Charles Henry Heiberg

Vol. 80 (1979), No. 1, 159–167
Abstract

Let f be defined on Tn and have an absolutely convergent Fourier series

f(eiσ) = Σfmeim ⋅σ.

Set f= Σ|fm|. In this paper sufficient conditions for fk= 0(1), as k →∞, are obtained.

Mathematical Subject Classification 2000
Primary: 42B05
Secondary: 43A20
Milestones
Received: 2 August 1977
Revised: 30 March 1978
Published: 1 January 1979
Authors
Charles Henry Heiberg