Proceedings of the American Mathematical Society

Author(s): Jean-Pierre Gabardo; Yun-Zhang Li
Journal: Proc. Amer. Math. Soc. 135 (2007), 1775-1784.
MSC (2000): Primary 42C40; Secondary 42C15
Posted: November 7, 2006
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Abstract: Given a $d\times d$ expansive dilation matrix

, a measurable set $E\subset \mathbb{R}^d$ is called a

-dilation generator of $\mathbb{R}^d$ if $\mathbb{R}^d$ is tiled (modulo null sets) by the collection $\{ (D^t)^j E,\,j\in \mathbb{Z}\}$ . Our main goal in this paper is to prove certain results relating the support of the Fourier transform of functions generating a wavelet or orthonormal affine system associated with the dilation

to an arbitrary set

which is a

-dilation generator of $\mathbb{R}^d$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42C40, 42C15

Jean-Pierre Gabardo
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Email: gabardo@mcmaster.ca

Yun-Zhang Li
Affiliation: Department of Applied Mathematics, Beijing University of Technology, Beijing, 100022, People's Republic of China
Email: yzlee@bjut.edu.cn

DOI: 10.1090/S0002-9939-06-08659-X
PII: S 0002-9939(06)08659-X
Keywords: Affine systems, wavelets, dilation generator
Received by editor(s): September 8, 2005
Received by editor(s) in revised form: February 2, 2006
Posted: November 7, 2006
Additional Notes: The first author was supported by an NSERC grant.
The second author was supported by the Natural Science Foundation of Beijing and the Foundation of Educational Ministry of China
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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