Fourier series with bounded convolution powers

Charles Henry Heiberg

Vol. 80 (1979), No. 1, 159–167

DOI: 10.2140/pjm.1979.80.159

Abstract

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

Set ∥f∥ = Σ|f_m|. In this paper sufficient conditions for ∥f^k∥ = 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