与非其次细分方程相关的细分格式的收敛阶

Convergence Rates of Subdivsion Schemes Associated with Inhomogeneous Refinement Equations

研究如下形式的方程:φ(x)=∑α∈Zsa(α)φ(Mx-α)+g(x)。定义φn=∑α∈Zsa(α)φn-1(Mx-α)+g(x),n=1,2,…。函数{φn}列称为细分格式。目的是刻画函数列{φn}在索伯列夫空间Wk2(Rs)中的收敛阶。

We consider following functional equation:φ(x)=∑α∈Z^sa(α)φ(Mx-α)+g(x).Define φ_n=∑α∈Zsa(α)φ_(n-1)(Mx-α)+g(x),x∈R^s,n=1,2,... . The function sequence {φ_n} is called subdivsion schemes. The purpose of this paper is to characterize the convergence rates of function sequence {φ_n}in Sobolev space W^k_2(R^s).