The Relationship between $\epsilon$-Kronecker and Sidon Sets

Abstract

A subset $E$ of a discrete abelian group is called $\epsilon$-Kronecker if all $E$-functions of modulus one can be approximated to within $\epsilon$ by characters. $E$ is called a Sidon set if all bounded $E$-functions can be interpolated by the Fourier transform of measures on the dual group. As $\epsilon$-Kronecker sets with $\epsilon <2$ possess the same arithmetic 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.

arXiv comment7 pages

Cited by in corpus (1)

• Sidon sets are proportionally Sidon with small Sidon constants