Title
Duality Questions For Operators, Spectrum And Measures
Keywords
Fractal; Hilbert space; Orthogonal basis; Spectrum; Tiling
Abstract
We explore spectral duality in the context of measures in ℝ n, starting with partial differential operators and Fuglede's question (1974) about the relationship between orthogonal bases of complex exponentials in L 2(Ω) and tiling properties of Ω, then continuing with affine iterated function systems. We review results in the literature from 1974 up to the present, and we relate them to a general framework for spectral duality for pairs of Borel measures in ℝ n, formulated first by Jorgensen and Pedersen. © 2009 Springer Science+Business Media B.V.
Publication Date
12-1-2009
Publication Title
Acta Applicandae Mathematicae
Volume
108
Issue
3
Number of Pages
515-528
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1007/s10440-008-9427-8
Copyright Status
Unknown
Socpus ID
71449123842 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/71449123842
STARS Citation
Dutkay, Dorin Ervin and Jorgensen, Palle E.T., "Duality Questions For Operators, Spectrum And Measures" (2009). Scopus Export 2000s. 11104.
https://stars.library.ucf.edu/scopus2000/11104