Vector-valued multiresolution analysis on local fields

摘要

In this paper, we study vector-valued multiresolution analysis on local fields of positive characteristic p. The associated subspace V_0 of L~2(K, C~N) has an orthonormal basis, a collection of translates of the scaling function φ of the form {φ(t - u(k))}_(k∈P), where P = {0,1,2,...}. We find the necessary and sufficient condition for the existence of associated wavelets.