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Subdivisions with infinitely supported mask
- Source :
-
Journal of Computational & Applied Mathematics . Apr2008, Vol. 214 Issue 1, p288-303. 16p. - Publication Year :
- 2008
-
Abstract
- Abstract: In this paper we investigate the convergence of subdivision schemes associated with masks being polynomially decay sequences. Two-scale vector refinement equations are the formwhere the vector of functions is in and is polynomially decay sequence of matrices called refinement mask. Associated with the mask a is a linear operator on given byBy using same methods in [B. Han, R. Q. Jia, Characterization of Riesz bases of wavelets generated from multiresolution analysis, manuscript]; [B. Han, Refinable functions and cascade algorithms in weighted spaces with infinitely supported masks, manuscript]; [R.Q. Jia, Q.T. Jiang, Z.W. Shen, Convergence of cascade algorithms associated with nonhomogeneous refinement equations, Proc. Amer. Math. Soc. 129 (2001) 415–427]; [R.Q. Jia, Convergence of vector subdivision schemes and construction of biorthogonal multiple wavelets, in: Advances in Wavelet, Hong Kong,1997, Springer, Singapore, 1998, pp. 199–227], a characterization of convergence of the sequences in the -norm is given, which extends the main results in [R.Q. Jia, S.D. Riemenschneider, D.X. Zhou, Vector subdivision schemes and multiple wavelets, Math. Comp. 67 (1998) 1533–1563] on convergence of the subdivision schemes associated with a finitely supported mask to the case in which mask a is polynomially decay sequence. As an application, we also obtain a characterization of smoothness of solutions of the refinement equation mentioned above for the case . [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*EQUATIONS
*ALGORITHMS
*OPERATOR theory
Subjects
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 214
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 29959732
- Full Text :
- https://doi.org/10.1016/j.cam.2007.02.033