|
On the characterization of scaling functions on non-Archimedean fields
Ishtaq Ahmed, Owias Ahmad, Neya Ahmad Sheikh National Institute of Technology, Srinagar, Jammu and Kashmir
Abstract:
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 L2(R). In this setting, the associated translation set Λ={0,r/N}+2Z 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 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.
Keywords:
scaling function, Fourier transform, local field, NUMRA.
Citation:
Ishtaq Ahmed, Owias Ahmad, Neya Ahmad Sheikh, “On the characterization of scaling functions on non-Archimedean fields”, Ural Math. J., 7:1 (2021), 3–15
Linking options:
https://www.mathnet.ru/eng/umj133 https://www.mathnet.ru/eng/umj/v7/i1/p3
|
Statistics & downloads: |
Abstract page: | 108 | Full-text PDF : | 55 | References: | 28 |
|