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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tight wavelet frames generated by three symmetric $B$-spline functions with high vanishing moments


Authors: Bin Han and Qun Mo
Journal: Proc. Amer. Math. Soc. 132 (2004), 77-86
MSC (2000): Primary 42C40, 41A15, 41A25
Published electronically: July 28, 2003
MathSciNet review: 2021250
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Abstract: In this note, we show that one can derive from any $B$-spline function of order $m$ ( $m\in \mathbb N$) an MRA tight wavelet frame in $L_2(\mathbb R)$ that is generated by the dyadic dilates and integer shifts of three compactly supported real-valued symmetric wavelet functions with vanishing moments of the highest possible order $m$.


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Additional Information

Bin Han
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: bhan@math.ualberta.ca

Qun Mo
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: mo@math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07205-8
PII: S 0002-9939(03)07205-8
Keywords: Symmetric tight wavelet frames, $B$-spline functions, vanishing moments
Received by editor(s): April 9, 2002
Published electronically: July 28, 2003
Additional Notes: Research was supported in part by NSERC Canada under Grant G121210654 and by Alberta Innovation and Science REE under Grant G227120136
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society