Title

Atomic representations of Cuntz algebras

Authors

Authors

D. E. Dutkay; J. Haussermann;P. E. T. Jorgensen

Comments

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Abbreviated Journal Title

J. Math. Anal. Appl.

Keywords

Iterated function system; Wavelet; Spectral measures; Cuntz algebras; Walsh bases; Permutative representations; ITERATED FUNCTION SYSTEMS; FRACTAL MEASURES; FOURIER-SERIES; WAVELETS; ENDOMORPHISMS; EXPANSIONS; ISOMETRIES; OPERATORS; STATES; SPACE; Mathematics, Applied; Mathematics

Abstract

To a representation of O-N (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 S. 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. (C) 2014 Published by Elsevier Inc.

Journal Title

Journal of Mathematical Analysis and Applications

Volume

421

Issue/Number

1

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

215

Last Page

243

WOS Identifier

WOS:000349939100014

ISSN

0022-247X

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