Vol. 41, No. 1, 1972

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Lacunarity for compact groups. II

Robert E. Edwards, Edwin Hewitt and Kenneth Allen Ross

Vol. 41 (1972), No. 1, 99–109

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
Received: 25 March 1971
Published: 1 April 1972
Robert E. Edwards
Edwin Hewitt
Kenneth Allen Ross