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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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On characterizations of multiwavelets in $L^{2}(\mathbb {R}^n)$
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by Marcin Bownik PDF
Proc. Amer. Math. Soc. 129 (2001), 3265-3274 Request permission

Abstract:

We present a new approach to characterizing (multi)wavelets by means of basic equations in the Fourier domain. Our method yields an uncomplicated proof of the two basic equations and a new characterization of orthonormality and completeness of (multi)wavelets.
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Additional Information
  • Marcin Bownik
  • Affiliation: Department of Mathematics, Washington University, Campus Box 1146, St. Louis, Missouri 63130
  • Address at time of publication: Department of Mathematics, University of Michigan, 525 East University Avenue, Ann Arbor, Michigan 48109-1109
  • MR Author ID: 629092
  • Email: marbow@math.wustl.edu, marbow@math.lsa.umich.edu
  • Received by editor(s): September 27, 1999
  • Received by editor(s) in revised form: March 10, 2000
  • Published electronically: March 29, 2001
  • Additional Notes: The author thanks Richard Rochberg, Ziemowit Rzeszotnik, and Darrin Speegle for helpful comments and the referee for apt questions leading to the improvement of the paper.
  • Communicated by: David R. Larson
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3265-3274
  • MSC (2000): Primary 42C40
  • DOI: https://doi.org/10.1090/S0002-9939-01-05942-1
  • MathSciNet review: 1845001