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

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**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.## References

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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