Vol. 9(2) July 2021, No. 25, pp. 295-307.

NONUNIFORM SEMI-ORTHOGONAL WAVELET FRAMES ON NON-ARCHIMEDEAN FIELDS
Vol. 9(2) July 2021, No. 25, pp. 295-307
OWAIS AHMAD AND NEYAZ A. SHEIKH

 

Abstract

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in L2 (R) was considered by Gabardo and Nashed (J Funct. Anal. 158:209-241, 1998). In this setting, the associated translation set Λ = {0, r/N} + 2 Z is no longer a discrete subgroup of R but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we introduce the notion of nonuniform semi-orthogonal wavelet frame associated with nonuniform frame multiresolution analysis on non-Archimedean fields and provide their characterization by means of some basic equations in the frequency domain.


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