Some properties of five-coefficient refinement equation

摘要

1. Introduction. The purpose of this paper is to study global linear independence, local linear independence and Holder continuity of the solution of the following refinement equation. were c0c4≠0 and to construct compactly supported wavelets of the multiresolution generated by O. Here the Fourier transform is deined by. for every integrable function f and its form in distribution sense is understood as usual.