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

 

On characterizations of multiwavelets in $L^{2}(\mathbb{R}^n)$


Author: Marcin Bownik
Journal: Proc. Amer. Math. Soc. 129 (2001), 3265-3274
MSC (2000): Primary 42C40
Published electronically: March 29, 2001
MathSciNet review: 1845001
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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
Email: marbow@math.wustl.edu, marbow@math.lsa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05942-1
PII: S 0002-9939(01)05942-1
Keywords: Bessel family, affine frame, quasi affine frame, (multi)wavelet
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
Article copyright: © Copyright 2001 American Mathematical Society