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Sidon Sets are Proportionally Sidon with Small Sidon Constants

Part of: Harmonic analysis in one variable Abstract harmonic analysis

Published online by Cambridge University Press:  11 December 2018

Kathryn E. Hare  and
Robert (Xu) Yang
Kathryn E. Hare
Affiliation:
Dept. of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada Email: kehare@uwaterloo.cayangxu_robert@hotmail.com
Robert (Xu) Yang
Affiliation:
Dept. of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada Email: kehare@uwaterloo.cayangxu_robert@hotmail.com
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Abstract

In his seminal work on Sidon sets, Pisier found an important characterization of Sidonicity: A set is Sidon if and only if it is proportionally quasi-independent. Later, it was shown that Sidon sets were proportionally “special” Sidon in several other ways. Here, we prove that Sidon sets in torsion-free groups are proportionally $n$-degree independent, a higher order of independence than quasi-independence, and we use this to prove that Sidon sets are proportionally Sidon with Sidon constants arbitrarily close to one, the minimum possible value.

Keywords

Sidon setindependent set

MSC classification

Primary: 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
Secondary: 42A55: Lacunary series of trigonometric and other functions; Riesz products
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 4 , December 2019 , pp. 798 - 809
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

This research was supported in part by NSERC grant 2016-03719. This paper is in final form and no version of it will be submitted for publication elsewhere.

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