Complex Analysis and Operator Theory

, Volume 9, Issue 3, pp 631–652

Multiresolution Analysis Through Low-Pass Filter on Local Fields of Positive Characteristic

Article

Abstract

The concept of wavelet basis on the integers can be generalized to a countable subset of a local field having positive characteristic by using a prime element of such a field. In this paper, we provide a characterization of first-stage discrete wavelet system on a countable subset of a local field of positive characteristic. Further, we obtain some results on refinement equation and refinement coefficients which provide sufficient conditions for a function to be a solution of the refinement equation and generate a multiresolution analysis on the local fields.

Keywords

Local field Wavelet Multiresolution analysis  Low-pass filter Wavelets on the integers 

Mathematics Subject Classification (2010)

Primary 42C40 Secondary 42C15 43A70 11S85 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Discipline of MathematicsIndian Institute of Technology IndoreIndoreIndia
  2. 2.Department of Mathematics and Statistics, School of Basic Sciences, Sam Higginbottom Institute of Agriculture, Technology and SciencesDeemed UniversityAllahabadIndia

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