Multiresolution analysis on local fields

In this paper, we first establish the fundamental framework of multiresolution on local field in wavelet analysis. Accurately, orthonormal systems consisting of integer translations of a single function φ∈L²(K) are characterized (Theorems 1 and 2), the concept of multiresolution analysis on local field (Definition 3) and construction of corresponding wavelet vectors (Theorem 3) are given. The definition of integral periodicity of a function on local field (Definition 4) is also given. An example is finally presented.