Spectral properties of the transition operator associated to a multivariate refinement equation

被引：23
|
作者：
Jia, RQ [1 ]
Zhang, SR [1 ]
机构：
[1] Univ Alberta, Dept Mat Sci, Edmonton, AB T6G 2G1, Canada
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 1999年 / 292卷 / 1-3期
基金：
加拿大自然科学与工程研究理事会;
关键词：
refinement equations; subdivision operators; transition operators; eigenvalues; invariant subspaces; approximation order; smoothness;
D O I：
10.1016/S0024-3795(99)00027-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given a finitely supported sequence a on Z(S) and an s x s dilation matrix M, the transition operator T-a is the linear operator defined by T(a)nu(alpha) := Sigma(B epsilon Zs) a(M alpha - beta)nu(beta), where alpha epsilon Z(s) and nu lies in l(0)(Z(s)), the linear space of all finitely supported sequences on Z(s), In this paper we investigate the spectral properties of the transition operator T-a and apply these properties to the study of the approximation and smoothness properties of the normalized solution of the refinement equation phi = Sigma(alpha epsilon Zs) a(alpha)phi(M . -x). (C) 1999 Elsevier Science Inc. All rights reserved.
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页码：155 / 178
页数：24
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