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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reducibility of the wavelet representation associated to the Cantor set


Authors: Dorin Ervin Dutkay and Sergei Silvestrov
Journal: Proc. Amer. Math. Soc. 139 (2011), 3657-3664
MSC (2010): Primary 42C40, 28D05, 47A67, 28A80
Published electronically: March 9, 2011
MathSciNet review: 2813395
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Abstract: We answer a question by Judith Packer about the irreducibility of the wavelet representation associated to the Cantor set. We prove that if the QMF filter does not have constant absolute value, then the wavelet representation is reducible.


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Additional Information

Dorin Ervin Dutkay
Affiliation: Department of Mathematics, University of Central Florida, 4000 Central Florida Boulevard, P.O. Box 161364, Orlando, Florida 32816-1364
Email: ddutkay@mail.ucf.edu

Sergei Silvestrov
Affiliation: Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden
Email: ssilvest@maths.lth.se

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10913-4
PII: S 0002-9939(2011)10913-4
Keywords: Wavelet representation, quadrature mirror filter, Cantor set
Received by editor(s): September 4, 2010
Published electronically: March 9, 2011
Additional Notes: Research supported in part by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT), the Swedish Research Council 621-2007-6338, the Swedish Royal Academy of Sciences and the Crafoord Foundation.
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.