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

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

doi:10.1016/j.exmath.2025.125662

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

Journal article

Peer reviewed

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

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

Expositiones mathematicae, Vol.44(1), 125662

02/2026

DOI: 10.1016/j.exmath.2025.125662

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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.

Details

Title: Subtitle: Fuglede’s conjecture, differential operators and unitary groups of local translations
Creators: Piyali Chakraborty - University of Central Florida
Dorin Ervin Dutkay - University of Central Florida
Palle E.T. Jorgensen - University of Iowa
Resource Type: Journal article
Publication Details: Expositiones mathematicae, Vol.44(1), 125662
DOI: 10.1016/j.exmath.2025.125662
ISSN: 0723-0869
Language: English
Electronic publication date: 02/2025
Date published: 02/2026
Academic Unit: Mathematics
Record Identifier: 9984790994802771

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