IRREDUCIBLE WAVELET REPRESENTATIONS AND ERGODIC AUTOMORPHISMS ON SOLENOIDS Academic Article

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.

authors

• Larson, David

published proceedings

• OPERATORS AND MATRICES

author list (cited authors)

• Dutkay, D. E., Larson, D. R., & Silvestrov, S.

citation count

• 5

complete list of authors

• Dutkay, Dorin Ervin||Larson, David R||Silvestrov, Sergei

publication date

• January 2011

publisher

• Element d.o.o.  Publisher

published in

• Operators and Matrices  Journal

keywords

• Cantor Set
• Ergodic Automorphism
• Refinable Function
• Representation
• Ruelle Operator
• Solenoid

Digital Object Identifier (DOI)

• 10.7153/oam-05-14

start page

• 201

end page

• 219

volume

• 5

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.7153%2Foam-05-14