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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
DOI: https://doi.org/10.1090/S0025-5718-2012-02592-0
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.


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

  • 1. K. Bittner, K. Urban, On interpolatory divergence-free wavelets, Math. Comp., 76 (2007), 903-929. MR 2291842 (2008b:42067)
  • 2. A. Cohen, Wavelet Methods in Numerical Analysis, Elsevier, 2003.
  • 3. D. L. Donoho, Interpolatory wavelet transforms, Preprint, 1992.
  • 4. R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer, New York, 1993. MR 1261635 (95f:41001)
  • 5. T. Hans, Theory of Function Spaces, Birkhauser, Besel, 1983. MR 781540 (86j:46026)
  • 6. W. H $ \ddot {\mbox {a}}$rdle, G. Kerkyacharian, D. Picard, A. Tsybakov, Wavelets, Approximation and Statistal Applications, Springer, 1998. MR 1618204 (99f:42065)
  • 7. R. Q. Jia, Approximation with scaled shift-invariant spaces by means of quasi-projection operators, J. Approx. Theory., 131 (2004), 30-46. MR 2103832 (2005h:41035)
  • 8. R. Q. Jia, Spline wavelets on the interval with homogeneous boundary conditions, Adv. Comput. Math., 30 (2009), 177-200. MR 2471447 (2009k:42073)
  • 9. R. Q. Jia, J. Z. Wang, D. X. Zhou, Compactly supported wavelets bases for Sobolev spaces, Appl. Comput. Harmon. Anal., 15 (2003), 224-241. MR 2010944 (2004h:42042)
  • 10. Q. Sun, Wiener's lemma for infinite matrices with polynomial off-diagonal decay, C. Acad. Sci. Paris, Ser I, 340 (2005), 567-570. MR 2138705 (2005m:42053)
  • 11. J. Zhao, Wavelet Characterizations for Besov Spaces, Ph. D Dissertation, Beijing University of Technology, P. R. China, 2010.

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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
Email: liuym@bjut.edu.cn

Junjian Zhao
Affiliation: Department of Mathematics, Tianjin Polytechnic University, 63 Chenglin Street, Hedong District, Tianjin 300160, People’s Republic of China
Email: zhaojunjian@emails.bjut.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-2012-02592-0
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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