Complex Analysis and Operator Theory

, Volume 9, Issue 3, pp 631–652

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



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.


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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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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