Multivariate refinement equations and convergence of cascade algorithms in L-p(0 < p < 1) spaces

CSpace

	Multivariate refinement equations and convergence of cascade algorithms in L-p(0 < p < 1) spaces
	Li, S
	2003
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	19 期号:1 页码:97-106
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.
关键词	inhomogeneous refinement equation joint spectral radius cascade algorithm L-p(R-S)(0 < p < 1) space
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000180848500010
出版者	SPRINGER-VERLAG BERLIN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18212
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.