Atomic representations of Cuntz algebras

    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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