p-Frame Multiresolution Analysis Related to the Walsh Functions

Shah, F.A.

Research Article

p-Frame Multiresolution Analysis Related to the Walsh Functions

F.A. Shah¹

Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India

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.

How to Cite

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

BibTeX

@article{Shah2015,
  author  = {Shah, F.A.},
  title   = {p-Frame Multiresolution Analysis Related to the Walsh Functions},
  journal = {Int. J. Anal. Appl.},
  volume  = {7},
  year    = {2015},
  pages   = {1--15},
  doi     = {}
}

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