Accuracy conditions of multivariate refinable vector in frequence domain

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	Accuracy conditions of multivariate refinable vector in frequence domain
	Chen, HL; Sheng, QH; Xiao, SL
	2001-02-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	41 期号:3-4 页码:461-481
摘要	Assume that Phi (x) = (Phi (1)(x),...,phi (r)(x))(inverted perpendicular), x is an element of R-d is a vector-valued function satisfying the refinement equation Phi (x) = Sigma (k is an element of Lambda) c(k)Phi (Ax - k) for some finite set Lambda of Z(d) and some r x r matrices ck. In [Ij, the requirements for Phi to have accuracy p are given in terms of some complicated matrix generated by mask. But how to characterize accuracy via symbol is an unsolved question in [I]. In this paper, we give accuracy conditions in frequency domain, i.e., conditions (1.19) and (1.20). By using accuracy conditions (1.19) and (1.20), we construct the superfunction which is very important to characterize approximation of shift-invariant space. Furthermore, we prove that (see Section 3) condition (1.19) is sufficient for refinable smooth functions to have accuracy p in the case of isotropic matrix dilation (i.e., (1.20) is redundant). (C) 2001 Elsevier Science Ltd. All rights reserved.
关键词	accuracy symbol refinable functions superfunction
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000166807700018
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16611
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, HL
作者单位	Acad Sinica, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, HL,Sheng, QH,Xiao, SL. Accuracy conditions of multivariate refinable vector in frequence domain[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2001,41(3-4):461-481.
APA	Chen, HL,Sheng, QH,&Xiao, SL.(2001).Accuracy conditions of multivariate refinable vector in frequence domain.COMPUTERS & MATHEMATICS WITH APPLICATIONS,41(3-4),461-481.
MLA	Chen, HL,et al."Accuracy conditions of multivariate refinable vector in frequence domain".COMPUTERS & MATHEMATICS WITH APPLICATIONS 41.3-4(2001):461-481.