Ishtaq Ahmed     (National Institute of Technology, Jammu and Kashmir, Srinagar-190006, India)
Owias Ahmad     (National Institute of Technology, Jammu and Kashmir, Srinagar-190006, India)
Neyaz Ahmad Sheikh     (National Institute of Technology, Jammu and Kashmir, Srinagar-190006, India)


In real life application all signals are not obtained from uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool.  This gap was filled by Gabardo and Nashed [11]   by establishing a constructive algorithm based on the theory of spectral pairs for constructing non-uniform wavelet basis in \(L^2(\mathbb R)\). In this setting, the associated translation set \(\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z\) is no longer a discrete subgroup of \(\mathbb R\) 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 characterize the scaling function for non-uniform multiresolution analysis on local fields of positive characteristic (LFPC). Some properties of wavelet scaling function associated with non-uniform multiresolution analysis (NUMRA) on LFPC are also established.


Scaling function, Fourier transform, Local field, NUMRA

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DOI: http://dx.doi.org/10.15826/umj.2021.1.001

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