Journal article
Harmonic analysis of iterated function systems with overlap
Journal of Mathematical Physics, Vol.48(8), p.83511
2007
DOI: 10.1063/1.2767004
Abstract
An iterated function system (IFS) is a system of contractive mappings τi:Y→Y, i=1,…,N (finite), where Y is a complete metric space. Every such IFS has a unique (up to scale) equilibrium measure (also called the Hutchinson measure μ), and we study the Hilbert space L2(μ). In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory and from subband filter operators in signal processing. These Cuntz-like operator systems were used in recent papers on wavelet analysis by Baggett, Jorgensen, Merrill, and Packer [Contemp. Math. 345, 11–25 (2004)], where they serve as a first step to generating wavelet bases of Parseval type (alias normalized tight frames), i.e., wavelet bases with redundancy. Similarly, it was shown in work by Dutkay and Jorgensen [Rev. Mat. Iberoam. 22, 131–180 (2006)] that the iterative operator approach works well for generating wavelets on fractals from IFSs without overla...
Details
- Title: Subtitle
- Harmonic analysis of iterated function systems with overlap
- Creators
- Palle E.T JorgensenKeri KornelsonKaren Shuman
- Resource Type
- Journal article
- Publication Details
- Journal of Mathematical Physics, Vol.48(8), p.83511
- DOI
- 10.1063/1.2767004
- ISSN
- 0022-2488
- eISSN
- 1089-7658
- Language
- English
- Date published
- 2007
- Academic Unit
- Mathematics
- Record Identifier
- 9983985840002771
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