Irreducible wavelet representations and ergodic automorphisms on solenoids

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

References in corpus (4)

• Martingales, endomorphisms, and covariant systems of operators in Hilbert space
• Compactly supported wavelets and representations of the Cuntz relations
• Hilbert spaces built on a similarity and on dynamical renormalization
• Reducibility of the wavelet representation associated to the Cantor set

Cited by in corpus (1)

• Reducibility of the wavelet representation associated to the Cantor set