Multiband Refinement Equation And Subdivision Schemes In L～p(R) Spaces

Let 1≤p≤∞, M≥3 be a fixed integer. A function φ∈ LP(R) is called an M - re finable fuction if @ satisfies some refinement equationfor some sequence a defined on Z. In this thesis, under the assumption that a is a finitely supported sequence on Z with a(a) = M, the Lp-convergence of thecorresponding subdivision scheme is characterized. Especially, the stability of the refinable function φ is not required herein.This thesis is organized as follows. In Chapter 1, some necessary definitions and notations, the background and main result of this thesis are given; In Chapter 2, some auxiliary lemmas and theorems are obtained; In Chapter 3, the main result is proved.