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Characterization of Low-pass Filters on Local Fields of Positive Characteristic

Published:2016-05-24
Printed: Sep 2016
• Qaiser Jahan,
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 208016, India
 Format: LaTeX MathJax PDF

Abstract

In this article, we give necessary and sufficient conditions on a function to be a low-pass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We use probability and martingale methods to provide such a characterization.
 Keywords: multiresolution analysis, local field, low-pass filter, scaling function, probability, conditional probability and martingales
 MSC Classifications: 42C40 - Wavelets and other special systems 42C15 - General harmonic expansions, frames 43A70 - Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05] 11S85 - Other nonanalytic theory

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