Vol. 71, No. 1, 1977

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Sidon sets associated with a closed subset of a compact abelian group

Earl Vern Dudley

Vol. 71 (1977), No. 1, 33–40

Déchamps-Gondim in [1] announced that a Sidon set E contained in the dual of a connected compact abelian group G is associated with each compact subset K of G having interior, in the sense that there exists a finite subset F of E and some constant such that this constant times the maximum absolute value of any E F-spectral trignometric polynomial on K majorizes the sum of the absolute values of the Fourier transform. It is readily shown that if G is not connected not all Sidon sets have this property. In [7], Ross described the class of all Sidon sets which are associated with all compact sets K having interior. In this paper, the Sidon sets associated with a particular set K are analysed and characterized.

Mathematical Subject Classification 2000
Primary: 43A46
Received: 2 November 1976
Published: 1 July 1977
Earl Vern Dudley