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Decomposition of wavelet representations and Martin boundaries
Mälardalen University, School of Education, Culture and Communication. (Matematik/tillämpad matematik)ORCID iD: 0000-0003-4554-6528
2012 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 262, no 3, 1043-1061 p.Article in journal (Refereed) Published
Abstract [en]

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. Published by Elsevier Inc.

Place, publisher, year, edition, pages
2012. Vol. 262, no 3, 1043-1061 p.
Keyword [en]
Irreducible representation, Wavelet, Martin boundary, Harmonic function
National Category
Mathematics Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-14332DOI: 10.1016/j.jfa.2011.10.010ISI: 000299127800009Scopus ID: 2-s2.0-84155170762OAI: oai:DiVA.org:mdh-14332DiVA: diva2:508898
Funder
Swedish Research Council, 20076338
Available from: 2012-03-16 Created: 2012-03-10 Last updated: 2017-12-07Bibliographically approved

Open Access in DiVA

arXiv:1105.3442v2 [math.FA](239 kB)185 downloads
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