Search: MSC category 42A55
( Lacunary series of trigonometric and other functions; Riesz products )
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||The relationship between $\epsilon$-Kronecker sets and Sidon sets|
A subset $E$ of a discrete abelian group is called $\epsilon
all $E$-functions of modulus one can be approximated to within
by characters. $E$ is called a Sidon set if all bounded $E$-functions
interpolated by the Fourier transform of measures on the dual
group. As $%
\epsilon $-Kronecker sets with $\epsilon \lt 2$ possess the same
properties as Sidon sets, it is natural to ask if they are Sidon.
We use the
Pisier net characterization of Sidonicity to prove this is true.
Keywords:Kronecker set, Sidon set
Categories:43A46, 42A15, 42A55