IRREDUCIBLE WAVELET REPRESENTATIONS AND ERGODIC AUTOMORPHISMS ON SOLENOIDS

    Authors

    D. E. Dutkay; D. R. Larson;S. Silvestrov

    Comments

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    Abbreviated Journal Title

    Oper. Matrices

    Keywords

    Representation; ergodic automorphism; Cantor set; Ruelle operator; solenoid; refinable function; LOW-PASS FILTERS; MULTIRESOLUTION ANALYSES; CONSTRUCTION; MARTINGALES; FRACTALS; Mathematics

    Abstract

    We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, introduced in [13], and we present several equivalent formulations of the problem.

    Journal Title

    Operators and Matrices

    Volume

    5

    Issue/Number

    2

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    201

    Last Page

    219

    WOS Identifier

    WOS:000291111800002

    ISSN

    1846-3886

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