p-Frame Multiresolution Analysis Related to the Walsh Functions

Abstract

A generalization of the notion of p-multiresoltion analysis on a half-line, based on the theory of shift-invariant spaces is considered. In contrast to the standard setting, the associated subspace V0 of L2 (R+) has a frame, a collection of translates of the scaling function ϕ of the form {ϕ(· k)}k∈Z+ , where Z+ is the set of non-negative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of p-frame multiresoltion analysis (p-FMRA) on positive half-line R+. Finally, we establish a complete characterization of all p-wavelet frames associated with p-FMRA on positive half-line R+ using the shift-invariant space theory.