Journal article
Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N
Integral Equations and Operator Theory, Vol.28(4), pp.382-443
1997
DOI: 10.1007/BF01309155
Abstract
In this paper we show how wavelets originating from multiresolution analysis of scale N give rise to certain representations of the Cuntz algebras O_N, and conversely how the wavelets can be recovered from these representations. The representations are given on the Hilbert space L^2(T) by (S_i\xi)(z)=m_i(z)\xi(z^N). We characterize the Wold decomposition of such operators. If the operators come from wavelets they are shifts, and this can be used to realize the representation on a certain Hardy space over L^2(T). This is used to compare the usual scale-2 theory of wavelets with the scale-N theory. Also some other representations of O_N of the above form called diagonal representations are characterized and classified up to unitary equivalence by a homological invariant.
Details
- Title: Subtitle
- Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N
- Creators
- Ola BratteliPalle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Integral Equations and Operator Theory, Vol.28(4), pp.382-443
- DOI
- 10.1007/BF01309155
- ISSN
- 0378-620X
- eISSN
- 1420-8989
- Language
- English
- Date published
- 1997
- Academic Unit
- Mathematics
- Record Identifier
- 9983985989102771
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