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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Reducibility of the wavelet representation associated to the Cantor set
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by Dorin Ervin Dutkay and Sergei Silvestrov PDF
Proc. Amer. Math. Soc. 139 (2011), 3657-3664 Request permission

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
  • MR Author ID: 608228
  • 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
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3657-3664
  • MSC (2010): Primary 42C40, 28D05, 47A67, 28A80
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10913-4
  • MathSciNet review: 2813395