Irreducible wavelet representations and ergodic automorphisms on solenoids
Functional Analysis
2010-11-08 v2
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.
Cite
@article{arxiv.0910.0870,
title = {Irreducible wavelet representations and ergodic automorphisms on solenoids},
author = {Dorin Ervin Dutkay and David R. Larson and Sergei Silvestrov},
journal= {arXiv preprint arXiv:0910.0870},
year = {2010}
}