Multiresolution analysis on local fields

On orthogonal systems of shifts of scaling function on local fields of positive characteristic

“…, which is a solution of refinement equation (8) and which satisfies conditions (10). Satisfying both conditions is the main difficulty of this problem.…”

“…Chinese mathematicians Jiang et al in the article [10] introduced the notion of multiresolution analysis (MRA) on local fields. For the fields F (s) of positive characteristic p they proved some properties and gave an algorithm for constructing wavelets for a known scaling function.…”

How to construct wavelets on local fields of positive characteristic

“…) form a wavelet system [10]. For a step refinable function we can describe an algorithm for constructing masks m (χ).…”

“…In 2004 H.Jiang, D.Li, and N.Jin [10] introduced the notion of multiresolution analysis (MRA) on local fields F (s) of positive characteristic p, proved some properties and constructed "Haar MRA" and corresponding "Haar wavelets". The wavelet theory developed in [1,2,3,4,11].…”

Continuous wavelet transform on local fields

“…A local field means an algebraic field and a topological space with the topological properties of locally compact, non-discrete, complete and totally disconnected, denoted by K [8]. The additive and multiplicative groups of K are denoted by K + and K * , respectively.…”