Holes in the spectrum of functions generating affine systems
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- by Jean-Pierre Gabardo and Yun-Zhang Li PDF
- Proc. Amer. Math. Soc. 135 (2007), 1775-1784 Request permission
Abstract:
Given a $d\times d$ expansive dilation matrix $D$, a measurable set $E\subset \mathbb {R}^d$ is called a $D^t$-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 $D$ to an arbitrary set $E$ which is a $D^t$-dilation generator of $\mathbb {R}^d$.References
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Additional Information
- Jean-Pierre Gabardo
- Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- MR Author ID: 269511
- 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
- Received by editor(s): September 8, 2005
- Received by editor(s) in revised form: February 2, 2006
- Published electronically: 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 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1775-1784
- MSC (2000): Primary 42C40; Secondary 42C15
- DOI: https://doi.org/10.1090/S0002-9939-06-08659-X
- MathSciNet review: 2286088