Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition-Reference-Cited by-同舟云学术

Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition

Published:2023-08-09 Issue: Volume: Page:
ISSN:0025-584X
Container-title:Mathematische Nachrichten
language:en
Short-container-title:Mathematische Nachrichten

Author:

Spindeler Timo¹,Strungaru Nicolae²³

Affiliation:

1. Fakultät für Mathematik Universität Bielefeld Bielefeld Germany

2. Department of Mathematical Sciences MacEwan University Edmonton Alberta Canada

3. Institute of Mathematics “Simon Stoilow,” Bucharest Romania

Abstract

AbstractIn this paper, we study the class of tempered distributions whose Fourier transform is a translation bounded measure and show that each such distribution in has order at most 2d. We show the existence of the generalized Eberlein decomposition within this class of distributions, and its compatibility with all previous Eberlein decompositions. The generalized Eberlein decomposition for Fourier transformable measures and properties of its components are discussed. Lastly, we take a closer look at the absolutely continuous spectrum of measures supported on Meyer sets.

Funder

Deutsche Forschungsgemeinschaft

Natural Sciences and Engineering Research Council of Canada

Publisher

Wiley

Subject

General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.202100658

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