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Cuntz–Krieger Algebras and Wavelets on Fractals

Marcolli, Matilde and Paolucci, Anna Maria (2011) Cuntz–Krieger Algebras and Wavelets on Fractals. Complex Analysis and Operator Theory, 5 (1). pp. 41-81. ISSN 1661-8254.

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We consider representations of Cuntz–Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron–Frobenius and Ruelle operators to construct families of wavelets on these Cantor sets.

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Additional Information:© 2011 Springer. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. Received: 6 August 2009; Accepted: 2 November 2009; Published online: 21 November 2009. Communicated by Palle Jorgensen. Part of this work was done during a stay of the authors at the Max Planck Institute for Mathematics, which we thank for the hospitality and support. M. Marcolli was partially supported by NSF grant DMS-0651925.
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Subject Keywords:Cuntz–Krieger; Wavelets; Fractals; Cantor set; Hilbert space; Perron–Frobenius operator; Ruelle operator
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Record Number:CaltechAUTHORS:20110322-095729744
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23044
Deposited By: Jason Perez
Deposited On:22 Mar 2011 20:39
Last Modified:03 Oct 2019 02:42

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