Journal article
Harmonic Analysis of Fractal Processes via C ‐ Algebras
Mathematische Nachrichten, Vol.200(1), pp.77-117
1999
DOI: 10.1002/mana.19992000105
Abstract
We construct a harmonic analysis of iteration systems which include those which arise from wavelet algorithms based on multiresolutions. While traditional discretizations lead to asymptotic formulas, we argue here for a direct Fourier duality; but it is based on a non ‐ commutative harmonic analysis, specifically on representations of the Cuntz C* ‐algebras. With this approach the waling from the wavelet takes the form of an endomorphism of B(H), H a Hilbert space derived from the lattice of translations. We use this to describe, and to calculate, new invariants for the wavelets. those iteration systems which arise from wavelets and from Julia sets, we show that the associated endomorphisms are in fact Powers shifts.
Details
- Title: Subtitle
- Harmonic Analysis of Fractal Processes via C ‐ Algebras
- Creators
- Palle E. T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Mathematische Nachrichten, Vol.200(1), pp.77-117
- DOI
- 10.1002/mana.19992000105
- ISSN
- 0025-584X
- eISSN
- 1522-2616
- Publisher
- WILEY‐VCH Verlag; Berlin
- Number of pages
- 41
- Language
- English
- Date published
- 1999
- Academic Unit
- Mathematics
- Record Identifier
- 9983986088902771
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