Multivariate refinement equation with nonnegative masks  

作　　者：LI Song & ZHOU Xinlong Department of Mathematics, Zhejiang University, Hangzhou 310027, China Instititute of Mathematics, University of Duisburg-Essen, D-47057, Duisburg, Germany 

出　　处：《Science China Mathematics》2006年第4期439-450,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10071071&10471123).

摘　　要：This paper is concerned with multivariate refinement equations of the type where (?) is the unknown function defined on the s-dimensional Euclidean space Rs, a is a finitely supported nonnegative sequence on Zs, and M is an s×s dilation matrix with m := |detM|. We characterize the existence of L2-solution of refinement equation in terms of spectral radius of a certain finite matrix or transition operator associated with refinement mask a and dilation matrix M. For s = 1 and M = 2, the sufficient and necessary conditions are obtained to characterize the existence of continuous solution of this refinement equation.This paper is concerned with multivariate refinement equations of the type ψ = ∑α∈Zs a(α)ψ(Mx - α),where ψ is the unknown function defined on the s-dimensional Euclidean space Rs, a is a finitely supported nonnegative sequence on Zs, and M is an s × s dilation matrix with m := |detM|. We characterize the existence of L2-solution of refinement equation in terms of spectral radius of a certain finite matrix or transition operator associated with refinement mask a and dilation matrix M. For s = 1 and M = 2, the sufficient and necessary conditions are obtained to characterize the existence of continuous solution of this refinement equation.

关 键 词：NONNEGATIVE mask  SUBDIVISION schemes  MULTIVARIATE REFINEMENT equation. 

分 类 号：O175[理学—数学]