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

1977; Mathematical Sciences Publishers; Volume: 71; Issue: 1 Linguagem: Inglês

10.2140/pjm.1977.71.33

1945-5844

E. Dudley,

Rings, Modules, and Algebras

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 i?\ i^-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.