Fuglede's conjecture, differential operators and unitary groups of local translations

Piyali Chakraborty; Dorin Ervin Dutkay; Palle E. T Jorgensen

doi:10.48550/arxiv.2410.03587

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Fuglede's conjecture, differential operators and unitary groups of local translations

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Fuglede's conjecture, differential operators and unitary groups of local translations

Piyali Chakraborty, Dorin Ervin Dutkay and Palle E. T Jorgensen

ArXiv.org

Cornell University

10/04/2024

DOI: 10.48550/arxiv.2410.03587

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Abstract

The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of L2 contexts where we make precise the interplay between the three sides of the question: (i) existence of orthogonal families of Fourier basis functions (and associated spectra) on the one hand, (ii) extensions of partial derivative operators, and (iii) geometry of the corresponding domains, stressing systems of translation-tiles. We emphasize an account of old and new developments since the original 1974-paper by Bent Fuglede where the co-authors and Steen Pedersen have contributed.

Mathematics - Functional Analysis

Details

Title: Subtitle: Fuglede's conjecture, differential operators and unitary groups of local translations
Creators: Piyali Chakraborty
Dorin Ervin Dutkay
Palle E. T Jorgensen
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2410.03587
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 10/04/2024
Academic Unit: Mathematics
Record Identifier: 9984721211602771

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