Title

Decomposition of wavelet representations and Martin boundaries

Authors

Authors

D. E. Dutkay; P. E. T. Jorgensen;S. Silvestrov

Comments

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Abbreviated Journal Title

J. Funct. Anal.

Keywords

Irreducible representation; Wavelet; Martin boundary; Harmonic function; GENERALIZED MULTIRESOLUTION ANALYSES; SYSTEMS; Mathematics

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.

Journal Title

Journal of Functional Analysis

Volume

262

Issue/Number

3

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

1043

Last Page

1061

WOS Identifier

WOS:000299127800009

ISSN

0022-1236

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