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.
