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An extension of Bittner and Urban's theorem

Authors: Youming Liu and Junjian Zhao
Journal: Math. Comp. 82 (2013), 401-411
MSC (2010): Primary 42C40, 35Q30, 41A15
Published electronically: June 5, 2012
MathSciNet review: 2983029
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Abstract: A class of Besov spaces are characterized by the quadratic and cubic Hermite multiwavelets (K. Bittner and K. Urban, On interpolatory divergence-free wavelets, Math. Comp., 76 (2007), 903-929). That characterization has a limitation, because of the regularity restriction of the Hermite splines. In this paper, we extend Bittner and Urban's theorem by using B-spline wavelets with weak duals introduced in the paper: R. Q. Jia, J. Z. Wang and D. X. Zhou, Compactly supported wavelet bases for Sobolev spaces, Appl. Comput. Harmon. Anal., 15 (2003), 224-241.

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Additional Information

Youming Liu
Affiliation: Department of Applied Mathematics, Beijing University of Technology, Pingle Yuan 100, Beijing 100124, People’s Republic of China

Junjian Zhao
Affiliation: Department of Mathematics, Tianjin Polytechnic University, 63 Chenglin Street, Hedong District, Tianjin 300160, People’s Republic of China

Keywords: Wavelet characterization, Besov spaces, completeness
Received by editor(s): August 11, 2009
Received by editor(s) in revised form: July 18, 2011
Published electronically: June 5, 2012
Additional Notes: This work is supported by the National Natural Science Foundation of China (No. 10871012) and the Natural Science Foundation of Beijing (No. 1082003).
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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