Orthonormal polynomial wavelets on the interval
HTML articles powered by AMS MathViewer
- by Dao-Qing Dai and Wei Lin PDF
- Proc. Amer. Math. Soc. 134 (2006), 1383-1390 Request permission
Abstract:
We use special functions and orthonormal wavelet bases on the real line to construct wavelet-like bases. With these wavelets we can construct polynomial bases on the interval; moreover, we can use them for the numerical resolution of degenerate elliptic operators.References
- S. Beuchler, R. Schneider, and C. Schwab, Multiresolution weighted norm equivalences and applications, Numer. Math. 98 (2004), no. 1, 67–97. MR 2076054, DOI 10.1007/s00211-003-0491-8
- C. K. Chui and H. N. Mhaskar, On trigonometric wavelets, Constr. Approx. 9 (1993), no. 2-3, 167–190. MR 1215768, DOI 10.1007/BF01198002
- Albert Cohen, Ingrid Daubechies, and Pierre Vial, Wavelets on the interval and fast wavelet transforms, Appl. Comput. Harmon. Anal. 1 (1993), no. 1, 54–81. MR 1256527, DOI 10.1006/acha.1993.1005
- Dao-Qing Dai, Wavelets and orthogonal polynomials based on harmonic oscillator eigenstates, J. Math. Phys. 41 (2000), no. 5, 3086–3103. MR 1755492, DOI 10.1063/1.533293
- Dao-Qing Dai, Bin Han, and Rong-Qing Jia, Galerkin analysis for Schrödinger equation by wavelets, J. Math. Phys. 45 (2004), no. 3, 855–869. MR 2036167, DOI 10.1063/1.1643541
- Daoqing Dai and Wei Lin, On the periodic orthonormal wavelet system, Acta Math. Sci. (English Ed.) 18 (1998), no. 1, 74–78. MR 1624061, DOI 10.1016/S0252-9602(17)30691-4
- Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107, DOI 10.1137/1.9781611970104
- Uwe Depczynski, Sturm-Liouville wavelets, Appl. Comput. Harmon. Anal. 5 (1998), no. 2, 216–247. MR 1614460, DOI 10.1006/acha.1997.0231
- Bernd Fischer and Jürgen Prestin, Wavelets based on orthogonal polynomials, Math. Comp. 66 (1997), no. 220, 1593–1618. MR 1423073, DOI 10.1090/S0025-5718-97-00876-4
- Michael Frazier and Shangqian Zhang, Bessel wavelets and the Galerkin analysis of the Bessel operator, J. Math. Anal. Appl. 261 (2001), no. 2, 665–691. MR 1853062, DOI 10.1006/jmaa.2001.7567
- Stéphane Jaffard, Wavelet methods for fast resolution of elliptic problems, SIAM J. Numer. Anal. 29 (1992), no. 4, 965–986. MR 1173180, DOI 10.1137/0729059
- T. Kilgore and J. Prestin, Polynomial wavelets on the interval, Constr. Approx. 12 (1996), no. 1, 95–110. MR 1389921, DOI 10.1007/s003659900004
Additional Information
- Dao-Qing Dai
- Affiliation: Department of Mathematics, Sun Yat-Sen (Zhongshan) University, Guangzhou, 510275 People’s Republic of China
- Email: stsddq@zsu.edu.cn
- Wei Lin
- Affiliation: Department of Mathematics, Sun Yat-Sen (Zhongshan) University, Guangzhou, 510275 People’s Republic of China
- Email: stslw@zsu.edu.cn
- Received by editor(s): December 8, 2004
- Published electronically: October 7, 2005
- Additional Notes: This research was partially supported by NSFC, EYTP, NSF of Guangdong and ZAAC
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1383-1390
- MSC (2000): Primary 42C40, 33C45, 42C10, 65L15
- DOI: https://doi.org/10.1090/S0002-9939-05-08088-3
- MathSciNet review: 2199184