Decomposition of wavelet representations and Martin boundaries
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
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.
Irreducible representation, Wavelet, Martin boundary, Harmonic function
Mathematics Mathematical Analysis
Research subject Mathematics/Applied Mathematics
IdentifiersURN: urn:nbn:se:mdh:diva-14332DOI: 10.1016/j.jfa.2011.10.010ISI: 000299127800009ScopusID: 2-s2.0-84155170762OAI: oai:DiVA.org:mdh-14332DiVA: diva2:508898
FunderSwedish Research Council, 20076338