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Ural Mathematical Journal, 2021, Volume 7, Issue 1, Pages 3–15
DOI: https://doi.org/10.15826/umj.2021.1.001
(Mi umj133)
 

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
References:
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.
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Document Type: Article
Language: English
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
Citation in format AMSBIB
\Bibitem{AhmAhmShe21}
\by Ishtaq~Ahmed, Owias~Ahmad, Neya~Ahmad~Sheikh
\paper On the characterization of scaling functions on non-Archimedean fields
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 1
\pages 3--15
\mathnet{http://mi.mathnet.ru/umj133}
\crossref{https://doi.org/10.15826/umj.2021.1.001}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4301209}
\zmath{https://zbmath.org/?q=an:1473.42042}
\elib{https://elibrary.ru/item.asp?id=46381210}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85111994798}
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