Open AccessConstruction of nonuniform periodic wavelet frames on non-Archimedean fields
Author(s) -
Owais Ahmad
Publication year - 2020
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2020.74.2.1-17
Subject(s) - wavelet , mathematics , dilation (metric space) , translation (biology) , fourier transform , pure mathematics , unitary state , spectral analysis , integer (computer science) , mathematical analysis , discrete mathematics , combinatorics , physics , computer science , quantum mechanics , biochemistry , chemistry , artificial intelligence , spectroscopy , messenger rna , political science , law , gene , programming language
In real life applications not all signals are obtained by uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool. Gabardo and Nashed, and Gabardo and Yu filled this gap by the concept of nonuniform multiresolution analysis and nonuniform wavelets based on the theory of spectral pairs for which the associated translation set \(\Lambda= \{0,r/N\}+2\mathbb{Z}\) 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 introduce a notion of nonuniform periodic wavelet frame on non-Archimedean field. Using the Fourier transform technique and the unitary extension principle, we propose an approach for the construction of nonuniform periodic wavelet frames on non-Archimedean fields.