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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The authors would like to thank the anonymous reviewer for his valuable comments and suggestions to improve the quality of the paper.
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Communicated by Palle Jorgensen.
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Shukla, N.K., Vyas, A. Multiresolution Analysis Through Low-Pass Filter on Local Fields of Positive Characteristic. Complex Anal. Oper. Theory 9, 631–652 (2015). https://doi.org/10.1007/s11785-014-0396-9
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DOI: https://doi.org/10.1007/s11785-014-0396-9