Decomposition of wavelet representations and Martin boundaries

    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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