Title

Spectral Measures And Cuntz Algebras

Keywords

Fourier bases; Fractal; Hilbert space; Iterated function system; Operator algebras; Selfsimilar; Spectrum

Abstract

We consider a family of measures μ supported in (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 L2(μ) consisting of complex exponentials, i.e., a Fourier basis corresponding to a discrete subset Γ in (d. Here we offer two computational devices for understanding the interplay between the possibilities for such sets Γ (spectrum) and the measures μ 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. © 2012 American Mathematical Society.

Publication Date

8-3-2012

Publication Title

Mathematics of Computation

Volume

81

Issue

280

Number of Pages

2275-2301

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0025-5718-2012-02589-0

Socpus ID

84864401967 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84864401967

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