Journal article
Spectral measures and Cuntz algebras
Mathematics of Computation, Vol.81(280), pp.2275-2301
2012
DOI: 10.1090/S0025-5718-2012-02589-0
Abstract
We consider a family of measures $\mu$ supported in $\br^d$ 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 $\Gamma$ in $\br^d$. 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 $\mathcal O_N$.
Details
- Title: Subtitle
- Spectral measures and Cuntz algebras
- Creators
- Dorin Ervin DutkayPalle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Mathematics of Computation, Vol.81(280), pp.2275-2301
- DOI
- 10.1090/S0025-5718-2012-02589-0
- ISSN
- 0025-5718
- eISSN
- 1088-6842
- Language
- English
- Date published
- 2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985921502771
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