Title

Duality Questions for Operators, Spectrum and Measures

Authors

Authors

D. E. Dutkay;P. E. T. Jorgensen

Comments

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Abbreviated Journal Title

Acta Appl. Math.

Keywords

Spectrum; Hilbert space; Orthogonal basis; Fractal; Tiling; SELF-AFFINE TILES; PARTIAL-DIFFERENTIAL OPERATORS; ITERATED FUNCTION; SYSTEMS; DENSE ANALYTIC SUBSPACES; WEYL-BERRY CONJECTURE; MOCK; FOURIER-SERIES; FUGLEDES CONJECTURE; SET CONJECTURE; FRACTAL DRUMS; UNIVERSAL SPECTRA; Mathematics, Applied

Abstract

We explore spectral duality in the context of measures in a"e (n) , starting with partial differential operators and Fuglede's question (1974) about the relationship between orthogonal bases of complex exponentials in L (2)(Omega) and tiling properties of Omega, 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 a"e (n) , formulated first by Jorgensen and Pedersen.

Journal Title

Acta Applicandae Mathematicae

Volume

108

Issue/Number

3

Publication Date

1-1-2009

Document Type

Article

DOI Link

http://dx.doi.org/10.1007/s10440-008-9427-8

Language

English

First Page

515

Last Page

528

WOS Identifier

WOS:000271941500004

ISSN

0167-8019

Recommended Citation

"Duality Questions for Operators, Spectrum and Measures" (2009). Faculty Bibliography 2000s. 1502.
https://stars.library.ucf.edu/facultybib2000/1502