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The Relationship Between ϵ-Kronecker Sets and Sidon Sets

Published online by Cambridge University Press:  20 November 2018

Kathryn Hare
Affiliation:
Dept. of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1 e-mail: kehare@uwaterloo.ca
L. Thomas Ramsey
Affiliation:
Dept. of Mathematics, University of Hawaii, Honolulu, HI 96822, USA e-mail: ramsey@math.hawaii.edu
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Abstract

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A subset $E$ of a discrete abelian group is called $\varepsilon$-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 $\varepsilon$-Kronecker sets with $\varepsilon \,<\,2$ 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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2016

References

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