Sobolev空间中与非齐次细分方程相关的细分格式的收敛阶

Convergence Rates of Subdivsion Schemes in Sobolev Spaces Associated with Nonhomogeneous Refinement Equations

研究如下形式的非齐次细分方程,其中向量值函数是未知的,g是给定的紧支集向量值函数,a 是一个具有有限长的r×r矩阵值序列,称为细分面具,M是一个s×s整数矩阵, 并且满足limn→∞M-n=0.我们在Sobolev空间(Wpk(Rs))r(1≤p≤∞)中研究与非齐次细分方程相关的细分格式的收敛性和收敛阶.选择具有紧支集向量值函数,定义n=1,2,….这个叠代过程称为细分格式(详见文献[1-29]).

The purpose of this paper is to investigate multivariate nonhomogeneous refinement equations of the form , x∈Rs, where the vector of functions is unknown, g is a given vector of compactly supported functions on Rs, a is a finitely supported sequence of r×r matrices called the refinement mask, and M is an s×s integer matrix such that limn→∞ M-n = 0. Our purpose is to consider the convergence and convergence rates of the subdivsion schemes in Sobolev Spaces (Wpk(Rs))r (1≤p≤∞) associated with nonhomogeneous refinement equations mentioned above. Let (?)0 be an initial vector of function in the Sobolev spaces (Wpk(Rs))r (1≤p≤∞). For n = 1,2,..., define ,x∈Rs. This iterative process is called the subdivsion schemes (see [1-29]).