Decomposition of wavelet representations and Martin boundaries
(2012) In Journal of Functional Analysis 262(3). p.1043-1061- 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,... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2355198
- author
- Dutkay, Dorin Ervin ; Jorgensen, Palle E. T. and Silvestrov, Sergei LU
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Irreducible representation, Wavelet, Martin boundary, Harmonic function
- in
- Journal of Functional Analysis
- volume
- 262
- issue
- 3
- pages
- 1043 - 1061
- publisher
- Academic Press
- external identifiers
-
- wos:000299127800009
- scopus:84155170762
- ISSN
- 0022-1236
- DOI
- 10.1016/j.jfa.2011.10.010
- language
- English
- LU publication?
- yes
- id
- 05e54e63-85dd-4081-ad8e-2f8b81919a79 (old id 2355198)
- date added to LUP
- 2016-04-01 13:45:02
- date last changed
- 2025-04-04 13:57:17
@article{05e54e63-85dd-4081-ad8e-2f8b81919a79,
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. Published by Elsevier Inc.}},
author = {{Dutkay, Dorin Ervin and Jorgensen, Palle E. T. and Silvestrov, Sergei}},
issn = {{0022-1236}},
keywords = {{Irreducible representation; Wavelet; Martin boundary; Harmonic function}},
language = {{eng}},
number = {{3}},
pages = {{1043--1061}},
publisher = {{Academic Press}},
series = {{Journal of Functional Analysis}},
title = {{Decomposition of wavelet representations and Martin boundaries}},
url = {{http://dx.doi.org/10.1016/j.jfa.2011.10.010}},
doi = {{10.1016/j.jfa.2011.10.010}},
volume = {{262}},
year = {{2012}},
}