Duality Questions for Operators, Spectrum and Measures

    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

    Language

    English

    First Page

    515

    Last Page

    528

    WOS Identifier

    WOS:000271941500004

    ISSN

    0167-8019

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