Journal article
Decomposition of wavelet representations and Martin boundaries
Journal of functional analysis, Vol.262(3), pp.1043-1061
2012
DOI: 10.1016/j.jfa.2011.10.010
Abstract
We study a decomposition problem for a class of unitary representations associated with wavelet analysis, wavelet representations, but our framework is wider and has applications to multi-scale expansions arising in dynamical systems theory for non-invertible endomorphisms. Our main results offer a direct integral decomposition for the general wavelet representation, and we solve a question posed by Judith Packer. This entails a direct integral decomposition of the general wavelet representation. We further give a detailed analysis of the measures contributing to the decomposition into irreducible representations. We prove results for associated Martin boundaries, relevant for the understanding of wavelet filters and induced random walks, as well as classes of harmonic functions.
Details
- Title: Subtitle
- Decomposition of wavelet representations and Martin boundaries
- Creators
- Dorin Ervin Dutkay - University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd, P.O. Box 161364, Orlando, FL 32816-1364, USAPalle E.T Jorgensen - University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA 52242-1419, USASergei Silvestrov - Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.262(3), pp.1043-1061
- DOI
- 10.1016/j.jfa.2011.10.010
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Grant note
- Swedish Foundation for International Cooperation in Research and Higher Education (STINT) 2007-6338 / Swedish Research Council
- Language
- English
- Date published
- 2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985990702771
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