Journal article
Early influences, the Fuglede question, spectrum vs tiling, and connection to related work by John von Neumann, Irving Segal, Marshall Stone, and David Shale
Sampling theory, signal processing, and data analysis, Vol.21(2), 33
12/2023
DOI: 10.1007/s43670-023-00074-6
Abstract
The purpose of this paper is to place the classical formulation of the Fuglede conjecture (i.e., spectrum in L2(Ω) vs tiling properties for Ω) in a wider context of general questions in inverse problems taking the form of links between spectrum and geometry. By “spectrum” we refer here to existence of an orthogonal multivariable Fourier expansions for L2(Ω) . We accomplish this with reference to the early history of the problem, i.e., the context of classical theorems (von Neumann, Stone, and Segal) dealing with spectral resolutions, orthogonal expansions, and the theory of commuting selfadjoint extensions for partial differential operators which are defined from systems of local coordinates in Ω .
Details
- Title: Subtitle
- Early influences, the Fuglede question, spectrum vs tiling, and connection to related work by John von Neumann, Irving Segal, Marshall Stone, and David Shale
- Creators
- Palle E. T. Jorgensen - Department of Mathematics, The University of Iowa
- Resource Type
- Journal article
- Publication Details
- Sampling theory, signal processing, and data analysis, Vol.21(2), 33
- Publisher
- Springer International Publishing
- DOI
- 10.1007/s43670-023-00074-6
- ISSN
- 2730-5716
- eISSN
- 2730-5724
- Language
- English
- Date published
- 12/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984505160002771
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