Lacunarity for compact groups. II

Robert E. Edwards, Edwin Hewitt and Kenneth Allen Ross

Vol. 41 (1972), No. 1, 99–109

DOI: 10.2140/pjm.1972.41.99

Abstract

Let G be a compact Abelian group with character group X. A standard characterization of Sidonicity of a subset P of X is given by the statement: if f ∈ C(G) and the Fourier transform f vanishes on X|P, then ∑ χ ∈ X|f(χ)| < ∞. In this paper, we show that the characterization remains intact if C(G) is replaced by any one of a large class of smaller function spaces on G. Extensions to compact non-Abelian groups are also given.

Mathematical Subject Classification 2000

Primary: 43A46

Milestones

Received: 25 March 1971

Published: 1 April 1972