Lacunarity for compact groups. II

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 [FORMULA PRESENTED] vanishes on X\P, then [FORMULA PRESENTED] 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. © 1972 Pacific Journal of Mathematics.