Irreducible wavelet representations and ergodic automorphisms on solenoids

Details Irreducible wavelet representations and ergodic automorphisms on solenoids Irreducible wavelet representations and ergodic automorphisms on solenoids

2009-10-05

arxiv.org/abs/0910.0870v2

Mathematics

Functional Analysis

Scientific paper

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 \cite{DuJo06b}, and we present several equivalent formulations of the problem.

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