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arXiv · 1506.07389

The Relationship between $ε$-Kronecker and Sidon Sets

Kathryn Hare·L. Thomas Ramsey
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Abstract

A subset $E$ of a discrete abelian group is called $ε$-Kronecker if all $E$-functions of modulus one can be approximated to within $ε$ 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 $ε$-Kronecker sets with $ε<2$ 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.

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Kathryn Hare, L. Thomas Ramsey. 2015-06-04. The Relationship between $ε$-Kronecker and Sidon Sets. https://doi.org/10.4153/cmb-2016-002-3

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