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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
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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 multiresolution analysis, local field, low-pass filter, scaling function, probability, conditional probability and martingales
MSC Classifications: 42C40, 42C15, 43A70, 11S85 show english descriptions Wavelets and other special systems
General harmonic expansions, frames
Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05]
Other nonanalytic theory
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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