Advanced

Decomposition of wavelet representations and Martin boundaries

Dutkay, Dorin Ervin; Jorgensen, Palle E. T. and Silvestrov, Sergei LU (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:
author
organization
publishing date
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
Elsevier
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
2012-02-24 09:04:19
date last changed
2017-01-01 05:51:23
@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},
  keyword      = {Irreducible representation,Wavelet,Martin boundary,Harmonic function},
  language     = {eng},
  number       = {3},
  pages        = {1043--1061},
  publisher    = {Elsevier},
  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},
  volume       = {262},
  year         = {2012},
}