Title

IRREDUCIBLE WAVELET REPRESENTATIONS AND ERGODIC AUTOMORPHISMS ON SOLENOIDS

Authors

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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