SPECTRAL MEASURES AND CUNTZ ALGEBRAS

    Authors

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

    Comments

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    Abbreviated Journal Title

    Math. Comput.

    Keywords

    Spectrum; Hilbert space; fractal; Fourier bases; selfsimilar; iterated; function system; operator algebras; COMPLEX HADAMARD-MATRICES; ITERATED FUNCTION SYSTEMS; LARGEST PRIME; FACTOR; MERSENNE NUMBERS; FRACTALS; REPRESENTATIONS; CONJECTURE; ISOMETRIES; OPERATORS; DIMENSION; Mathematics, Applied

    Abstract

    We consider a family of measures p, supported in R-d and generated in the sense of Hutchinson by a finite family of affine transformations. It is known that interesting sub-families of these measures allow for an orthogonal basis in L-2(mu) consisting of complex exponentials, i.e., a Fourier basis corresponding to a discrete subset F in R-d. Here we offer two computational devices for understanding the interplay between the possibilities for such sets Gamma (spectrum) and the measures mu themselves. Our computations combine the following three tools: duality, discrete harmonic analysis, and dynamical systems based on representations of the Cuntz C*-algebras O-N.

    Journal Title

    Mathematics of Computation

    Volume

    81

    Issue/Number

    280

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    2275

    Last Page

    2301

    WOS Identifier

    WOS:000309315200016

    ISSN

    0025-5718

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