Bohr Sets in Triple Products of Large Sets in Amenable Groups

Bohr Sets in Triple Products of Large Sets in Amenable Groups J Fourier Anal Appl https://doi.org/10.1007/s00041-018-9615-5 Bohr Sets in Triple Products of Large Sets in Amenable Groups 1 2 Michael Björklund · John T. Griesmer Received: 28 March 2017 / Revised: 3 April 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We answer a question of Hegyvári and Ruzsa concerning effective estimates of the Bohr-regularity of certain triple sums of sets with positive upper Banach densities in the integers. Our proof also works for any discrete amenable group, and it does not require all addends in the triple products we consider to have positive (left) upper Banach densities; one of the addends is allowed to only have positive upper asymptotic density with respect to a (possibly very sparse) ergodic sequence. Keywords Bohr sets · Densities · Measurable recurrence 1 Main Results Let Γ be a discrete group. If (W, σ) is a finite-dimensional unitary Γ-representation, we define the (possibly trivial) semi-norm | · | on Γ by |γ| = sup σ(γ)w − w : w = 1 ,for γ ∈ Γ, W W Communicated by Hans G. Feichtinger. B John T. Griesmer jtgriesmer@gmail.com Michael Björklund micbjo@chalmers.se Department of Mathematics, Chalmers, Gothenburg, Sweden Department of Applied Mathematics http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Fourier Analysis and Applications Springer Journals

Bohr Sets in Triple Products of Large Sets in Amenable Groups

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics
ISSN
1069-5869
eISSN
1531-5851
D.O.I.
10.1007/s00041-018-9615-5
Publisher site
See Article on Publisher Site

Abstract

J Fourier Anal Appl https://doi.org/10.1007/s00041-018-9615-5 Bohr Sets in Triple Products of Large Sets in Amenable Groups 1 2 Michael Björklund · John T. Griesmer Received: 28 March 2017 / Revised: 3 April 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We answer a question of Hegyvári and Ruzsa concerning effective estimates of the Bohr-regularity of certain triple sums of sets with positive upper Banach densities in the integers. Our proof also works for any discrete amenable group, and it does not require all addends in the triple products we consider to have positive (left) upper Banach densities; one of the addends is allowed to only have positive upper asymptotic density with respect to a (possibly very sparse) ergodic sequence. Keywords Bohr sets · Densities · Measurable recurrence 1 Main Results Let Γ be a discrete group. If (W, σ) is a finite-dimensional unitary Γ-representation, we define the (possibly trivial) semi-norm | · | on Γ by |γ| = sup σ(γ)w − w : w = 1 ,for γ ∈ Γ, W W Communicated by Hans G. Feichtinger. B John T. Griesmer jtgriesmer@gmail.com Michael Björklund micbjo@chalmers.se Department of Mathematics, Chalmers, Gothenburg, Sweden Department of Applied Mathematics

Journal

Journal of Fourier Analysis and ApplicationsSpringer Journals

Published: May 31, 2018

References

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