Table of Contents
Journal of Operators
Volume 2015, Article ID 216060, 8 pages
http://dx.doi.org/10.1155/2015/216060
Research Article

Frame Multiresolution Analysis on Local Fields of Positive Characteristic

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

Received 21 August 2014; Accepted 12 January 2015

Academic Editor: Gerd Teschke

Copyright © 2015 Firdous A. Shah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspace of has a frame, a collection of translates of the scaling function of the form , where is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field of positive characteristic using the shift-invariant space theory.