Multivariate refinement equations and convergence of cascade algorithms in L-p(0 < p < 1) spaces
文献类型：期刊论文
| 作者 | Li, S |
| 刊名 | ACTA MATHEMATICA SINICA-ENGLISH SERIES
 |
| 出版日期 | 2003 |
| 卷号 | 19期号:1页码:97-106 |
| 关键词 | inhomogeneous refinement equation joint spectral radius cascade algorithm L-p(R-S)(0 < p < 1) space |
| ISSN号 | 1439-8516 |
| 英文摘要 | We consider the solutions of refinement equations written in the form phi(x)- Sigma(alphais an element ofZs) a(alpha)phi(Mx - alpha) + g(x), x is an element of R-s, where the vector of functions phi = (phi(1),...,phi(r))(T) is unknown, g is a given vector of compactly supported functions on R-s, a is a finitely supported sequence of r x r matrices called the refinement mask, and M is an s x s dilation matrix with m = \detM\. Inhomogeneous refinement equations appear in the constructions of multiwavelets and the constructions of wavelets on a finite interval. The cascade algorithm with mask a, g, and dilation M generates a sequence phi(n), n = 1, 2,..., by the iterative process phi(n)(x) = Sigma(alphais an element ofZs) a(alpha)phi(n-1) (Mx - alpha) + g(x), x is an element of R-s, from a starting vector of function WO. We characterize the L-p-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness property of the solutions of the refinement equations associated with the homogeneous refinement equation. |
| 语种 | 英语 |
| WOS记录号 | WOS:000180848500010 |
| 出版者 | SPRINGER-VERLAG BERLIN |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/18211]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Li, S |
| 作者单位 | 1.Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China 2.Chinese Acad Sci, Math Inst, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, S. Multivariate refinement equations and convergence of cascade algorithms in L-p(0 < p < 1) spaces[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2003,19(1):97-106. |
| APA | Li, S.(2003).Multivariate refinement equations and convergence of cascade algorithms in L-p(0 < p < 1) spaces.ACTA MATHEMATICA SINICA-ENGLISH SERIES,19(1),97-106. |
| MLA | Li, S."Multivariate refinement equations and convergence of cascade algorithms in L-p(0 < p < 1) spaces".ACTA MATHEMATICA SINICA-ENGLISH SERIES 19.1(2003):97-106. |
入库方式： OAI收割
来源：数学与系统科学研究院
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