0 . 08 70 v 2 [ m at h . FA ] 5 N ov 2 01 0 IRREDUCIBLE WAVELET REPRESENTATIONS AND ERGODIC AUTOMORPHISMS ON SOLENOIDS
نویسنده
چکیده
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 [DJ06a], and we present several equivalent formulations of the problem.
منابع مشابه
ar X iv : 0 71 0 . 31 19 v 2 [ m at h . G R ] 2 5 N ov 2 00 8 PRODUCT GROUPS ACTING ON MANIFOLDS
We analyse volume-preserving actions of product groups on Riemannian manifolds. To this end, we establish a new superrigidity theorem for ergodic cocycles of product groups ranging in linear groups. There are no a priori assumptions on the acting groups, except a spectral gap assumption on their action. Our main application to manifolds concerns irreducible actions of Kazhdan product groups. We...
متن کاملInduced representations arising from a character
Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from noncommutative harmonic analysis, ergodic theory, and dynamical systems. Our analysis is in the setting of semidirect products, discrete subgroups, and solenoids. Our applications include analysis an...
متن کاملRelations between positive definite functions and irreducible representations on a locally compact groupoid
If G is a locally compact groupoid with a Haar system λ, then a positive definite function p on G has a form p(x) = 〈L(x)ξ(d(x)), ξ(r(x))〉, where L is a representation of G on a Hilbert bundle H = (G, {Hu}, μ), μ is a quasi invariant measure on G 0 and ξ ∈ L(G,H). [10]. In this paper firt we prove that if μ is a quasi invariant ergodic measure on G, then two corresponding representations of G a...
متن کاملSymbolic Representations of Nonexpansive Group Automorphisms
If α is an irreducible nonexpansive ergodic automorphism of a compact abelian group X (such as an irreducible nonhyperbolic ergodic toral automorphism), then α has no finite or infinite state Markov partitions, and there are no nontrivial continuous embeddings of Markov shifts in X. In spite of this we are able to construct a symbolic space V and a class of shift-invariant probability measures ...
متن کاملPartition Functions for Statistical Mechanics with Micropartitions and Phase Transitions
X iv :c on dm at /0 41 11 76 v1 [ co nd -m at .s ta tm ec h] 7 N ov 2 00 4 PARTITION FUNCTIONS FOR STATISTICAL MECHANICS WITH MICROPARTITIONS AND PHASE TRANSITIONS AJAY PATWARDHAN Physics department, St Xavier’s college, Mahapalika Marg , Mumbai 400001,India Visitor, Institute of Mathematical Sciences, CIT campus, Tharamani, Chennai, India [email protected] ABSTRACT The fundamentals of Statistic...
متن کامل