Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Cube-approximating bounded wavelet sets in $\mathbb{R} ^{n}$

Author: Xiaojiang Yu
Journal: Proc. Amer. Math. Soc. 134 (2006), 491-499
MSC (2000): Primary 42C15
Published electronically: July 8, 2005
MathSciNet review: 2176018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

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

Retrieve articles in all journals with MSC (2000): 42C15

Additional Information

Xiaojiang Yu
Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1

Keywords: Real expansive matrix, bounded wavelet set, band-limited wavelet
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
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society