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A Non-abelian, Non-Sidon, Completely Bounded $\Lambda (p)$ Set

Part of: Abstract harmonic analysis Harmonic analysis in one variable

Published online by Cambridge University Press:  26 February 2020

Kathryn E. Hare  and
Parasar Mohanty
Kathryn E. Hare*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada
Parasar Mohanty
Affiliation:
Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India, 208016 e-mail: parasar@iitk.ac.in
*
e-mail: kehare@uwaterloo.ca
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Abstract

The purpose of this note is to construct an example of a discrete non-abelian group G and a subset E of G, not contained in any abelian subgroup, that is a completely bounded $\Lambda (p)$ set for all $p<\infty ,$ but is neither a Leinert set nor a weak Sidon set.

Keywords

Completely boundedSidon setnon-amenable group

MSC classification

Primary: 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Secondary: 42A55: Lacunary series of trigonometric and other functions; Riesz products
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 1 - 7
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Copyright
© Canadian Mathematical Society 2020

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