Approximation properties of wavelets on p-adic fields

Abstract

Refinable functions play an important role in the construction and properties of wavelets. Basically, most of the wavelets are generated from refinable functions. In this paper, a study on the approximation properties of refinable functions on [Formula: see text]-adic fields is carried out with necessary theoretical background. Various equivalent forms of approximation order and the connection between the approximation order and the Strang–Fix condition are derived. Finally a characterization for the approximation order of a refinable function is given in terms of order of the sum rules associated with the refinement mask.