Study of Linear Independence and Accuracy of Scaling Vectors via Two-scale Factors
作者： Hong Kong , Jianzhong Wang
DOI:
关键词: Invertible matrix 、 Scale (ratio) 、 Matrix (mathematics) 、 Matrix polynomial 、 Mathematics 、 Linear independence 、 Scaling 、 Discrete mathematics 、 Distribution (mathematics) 、 Combinatorics 、 Polynomial matrix
摘要: A scaling vector φ = (φ1, · , φr) is a compactly supported vector-valued distribution that satisfies matrix refinement equation φ(x) P Pkφ(2x−k), where (Pk) finite sequence. We call (z) 1 2 Pkz k the symbol of φ. said to be two-scale similar polynomial Q(z) if there an invertible T (z2)Q(z)T−1(z). called factor (z). In this paper we characterize linear independence and accuracy associated with via its symbol. The necessary sufficient conditions for either or are given. relation between them also revealed.
shsu.edu 参考文章(40)
T. N. T. Goodman, S. L. Lee, W. S. Tang, Wavelets in wandering subspaces Transactions of the American Mathematical Society. ,vol. 338, pp. 639- 654 ,(1993) , 10.1090/S0002-9947-1993-1117215-0
G. Plonka, Approximation order provided by refinable function vectors Constructive Approximation. ,vol. 13, pp. 221- 244 ,(1997) , 10.1007/BF02678465
David K. Ruch, Wasin So, Jianzhong Wang, Global Support of a Scaling Vector Applied and Computational Harmonic Analysis. ,vol. 5, pp. 493- 498 ,(1998) , 10.1006/ACHA.1998.0244
Thomas A. Hogan, Stability and independence of the shifts of finitely many refinable functions The Journal of Fourier Analysis and Applications. ,vol. 3, pp. 757- 774 ,(1997) , 10.1007/BF02648266
Rong-Qing Jia, S. D. Riemenschneider, Ding-Xuan Zhou, Vector subdivision schemes and multiple wavelets Mathematics of Computation. ,vol. 67, pp. 1533- 1563 ,(1998) , 10.1090/S0025-5718-98-00985-5
Carl de Boor, Amos Ron, Fourier analysis of the approximation power of principal shift-invariant spaces Constructive Approximation. ,vol. 8, pp. 427- 462 ,(1992) , 10.1007/BF01203462
Peter R. Massopust, David K. Ruch, Patrick J. Van Fleet, On the Support Properties of Scaling Vectors Applied and Computational Harmonic Analysis. ,vol. 3, pp. 229- 238 ,(1996) , 10.1006/ACHA.1996.0018
Charles K. Chui, Jian-zhong Wang, On compactly supported spline wavelets and a duality principle Transactions of the American Mathematical Society. ,vol. 330, pp. 903- 915 ,(1992) , 10.1090/S0002-9947-1992-1076613-3
Rong-Qing Jia, Charles A. Micchelli, On linear independence for integer translates of a finite number of functions Proceedings of the Edinburgh Mathematical Society. ,vol. 36, pp. 69- 85 ,(1993) , 10.1017/S0013091500005903
Ding-Xuan Zhou, Existence of multiple refinable distributions. The Michigan Mathematical Journal. ,vol. 44, pp. 317- 329 ,(1997) , 10.1307/MMJ/1029005707