Atomic Representations Of Cuntz Algebras

Keywords

Cuntz algebras; Iterated function system; Permutative representations; Spectral measures; Walsh bases; Wavelet

Abstract

To a representation of ON (the Cuntz algebra with N generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators Si*. We classify the purely atomic representations and find when such representations are permutative. Applications include: wavelet representations, representations generated by finitely correlated states, representation associated to Hadamard triples (or fractal spectral measures) and representations associated to generalized Walsh bases.

Publication Date

1-1-2015

Publication Title

Journal of Mathematical Analysis and Applications

Volume

421

Issue

1

Number of Pages

215-243

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmaa.2014.07.005

Socpus ID

84925810056 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84925810056

This document is currently not available here.

Share

COinS