Song LI(1), Jian Ping LIU(2),
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]).
