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.
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