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

Socpus ID

71449123842 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/71449123842

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