p-Frame Multiresolution Analysis Related to the Walsh Functions

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F.A. Shah, p-Frame Multiresolution Analysis Related to the Walsh Functions, Int. J. Anal. Appl., 7 (1) (2015), 1-15.

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F.A. Shah

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.

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