The momentum operator on a union of intervals and the Fuglede conjecture

Dorin Ervin Dutkay; Palle E. T Jorgensen

doi:10.48550/arxiv.2301.11377

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The momentum operator on a union of intervals and the Fuglede conjecture

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The momentum operator on a union of intervals and the Fuglede conjecture

Dorin Ervin Dutkay and Palle E. T Jorgensen

ArXiv.org

01/26/2023

DOI: 10.48550/arxiv.2301.11377

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

The purpose of the present paper is to place a number of geometric (and hands-on) configurations relating to spectrum and geometry inside a general framework for the {\it Fuglede conjecture}. Note that in its general form, the Fuglede conjecture concerns general Borel sets $\Omega$ in a fixed number of dimensions $d$ such that $\Omega$ has finite positive Lebesgue measure. The conjecture proposes a correspondence between two properties for $\Omega$, one takes the form of spectrum, while the other refers to a translation-tiling property. We focus here on the case of dimension one, and the connections between the Fuglede conjecture and properties of the self-adjoint extensions of the momentum operator $\frac{1}{2\pi i}\frac{d}{dx}$, realized in $L^2$ of a union of intervals.

Details

Title: Subtitle: The momentum operator on a union of intervals and the Fuglede conjecture
Creators: Dorin Ervin Dutkay
Palle E. T Jorgensen
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2301.11377
ISSN: 2331-8422
Language: English
Date posted: 01/26/2023
Academic Unit: Mathematics
Record Identifier: 9984363379502771

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