On Construction of Bounded Sets Not Admitting a General Type of Riesz Spectrum-Reference-Cited by-同舟云学术

On Construction of Bounded Sets Not Admitting a General Type of Riesz Spectrum

Published:2024-01-05 Issue:1 Volume:13 Page:36
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Lee Dae Gwan¹^ORCID

Affiliation:

1. Department of Mathematics and Big Data Science, Kumoh National Institute of Technology, Gumi 39177, Gyeongsangbuk-do, Republic of Korea

Abstract

We construct a bound set that does not admit a Riesz spectrum containing a nonempty periodic set for which the period is a rational multiple of a fixed constant. As a consequence, we obtain a bounded set V with an arbitrarily small Lebesgue measure such that for any positive integer N, the set of exponentials with frequencies in any union of cosets of NZ cannot be a frame for the space of square integrable functions over V. These results are based on the proof technique of Olevskii and Ulanovskii from 2008.

Funder

National Research Foundation of Korea (NRF) grant funded by the Korean government

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/13/1/36/pdf

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