Cube-approximating bounded wavelet sets in $\mathbb {R}^{n}$
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Abstract:
We prove that for any real expansive $n\times n$ matrix $A$, there exists a bounded $A$-dilation wavelet set in the frequency domain $\mathbb {R}^{n}$ (the inverse Fourier transform of whose characteristic function is a band-limited single wavelet in the time domain $\mathbb {R}^{n}$). Moreover these wavelet sets can approximate a cube in $\mathbb {R}^{n}$ arbitrarily. This result improves Dai, Larson and Speegle’s result about the existence of (basically unbounded) wavelet sets for real expansive matrices.References
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Additional Information
- Xiaojiang Yu
- Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1
- Email: yuxia@math.mcmaster.ca
- Received by editor(s): March 22, 2004
- Received by editor(s) in revised form: September 27, 2004
- Published electronically: July 8, 2005
- Additional Notes: The author thanks his supervisor Prof. Jean-Pierre Gabardo for valuable suggestions to revise the primitive results of this paper. The author also thanks Dr. Deguang Han for providing several helpful related preprints.
- Communicated by: David R. Larson
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 491-499
- MSC (2000): Primary 42C15
- DOI: https://doi.org/10.1090/S0002-9939-05-08037-8
- MathSciNet review: 2176018