Journal article
Compactly supported wavelets and representations of the Cuntz relations
Applied and computational harmonic analysis, Vol.8(2), pp.166-196
12/15/1999
DOI: 10.1006/acha.2000.0283
Abstract
Applied and Computational Harmonic Analysis 8 (2000), 166--196. We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polynomials are parametrized by the circle, and we compute that the corresponding filters generate irreducible mutually disjoint representations of of the Cuntz algebra $ O_{2} $ except at two points on the circle. One of the two exceptional points corresponds to the Haar wavelet and the other is the unique point on the circle where the father function defines a tight frame which is not an orthonormal basis. At these two points the representation decomposes into two and three mutually disjoint irreducible representations, respectively, and the two representations at the Haar point are each unitarily equivalent to one of the three representations at the other singular point.
Details
- Title: Subtitle
- Compactly supported wavelets and representations of the Cuntz relations
- Creators
- Ola BratteliDavid E EvansPalle E. T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Applied and computational harmonic analysis, Vol.8(2), pp.166-196
- DOI
- 10.1006/acha.2000.0283
- ISSN
- 1063-5203
- eISSN
- 1096-603X
- Language
- English
- Date published
- 12/15/1999
- Academic Unit
- Mathematics
- Record Identifier
- 9983985930902771
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