Journal article
The momentum operator on a union of intervals and the Fuglede conjecture
Sampling theory, signal processing, and data analysis, Vol.21(2), 34
12/2023
DOI: 10.1007/s43670-023-00072-8
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
Fuglede conjecture
. Note that in its general form, the Fuglede conjecture concerns general Borel sets
Ω
in a fixed number of dimensions
d
such that
Ω
has finite positive Lebesgue measure. The conjecture proposes a correspondence between two properties for
Ω
, 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
1
2
π
i
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 - University of Central FloridaPalle E. T. Jorgensen - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Sampling theory, signal processing, and data analysis, Vol.21(2), 34
- Publisher
- Springer International Publishing
- DOI
- 10.1007/s43670-023-00072-8
- ISSN
- 2730-5716
- eISSN
- 2730-5724
- Language
- English
- Date published
- 12/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984508460302771
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