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
Copyright Status
Unknown
Socpus ID
84925810056 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84925810056
STARS Citation
Dutkay, Dorin Ervin; Haussermann, John; and Jorgensen, Palle E.T., "Atomic Representations Of Cuntz Algebras" (2015). Scopus Export 2015-2019. 538.
https://stars.library.ucf.edu/scopus2015/538