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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
DOI: https://doi.org/10.1090/S0002-9939-03-07205-8
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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  • 1. C. K. Chui and W. He, Compactly supported tight frames associated with refinable functions, Appl. Comp. Harmonic Anal., 8 (2000), 293-319. MR 2001h:42049
  • 2. C. K. Chui, W. He, and J. Stöckler, Compactly supported tight and sibling frames with maximum vanishing moments, Appl. Comput. Harmonic Anal., 13 (2002), 224-262.
  • 3. I. Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, 61, SIAM, Philadelphia, 1992. MR 93e:42045
  • 4. I. Daubechies, B. Han, A. Ron, and Z. W. Shen, Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmonic Anal., 14 (2003), No. 1, 1-46.
  • 5. B. Han, On dual wavelet tight frames, Appl. Comput. Harmonic Anal., 4 (1997), 380-413. MR 98h:42031
  • 6. D. G. Han and D. R. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc. 147 (2000). MR 2001a:47013
  • 7. E. Hernández and G. Weiss, A first course on wavelets, CRC Press, Boca Raton, FL, 1996. MR 97i:42015
  • 8. A. Petukhov, Symmetric framelets, preprint, (2001).
  • 9. A. Ron and Z. W. Shen, Affine systems in $L_2(\mathbb{R} ^d)$: the analysis of the analysis operator, J. Funct. Anal., 148 (2) (1997), 408-447. MR 99g:42043

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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: https://doi.org/10.1090/S0002-9939-03-07205-8
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

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