Wave packet systems on local fields

In this paper, we introduce the notion of wave packet systems on local fields of positive characteristic and derive some characterizations of these systems by means of two basic equations in the Fourier domain. More precisely, we establish a complete characterization of orthogonal wave packet system...

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Bibliographic Details
Published inJournal of geometry and physics Vol. 120; pp. 5 - 18
Main Authors Shah, Firdous A., Ahmad, Owais
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2017
Subjects
Fourier transform
Gabor frame
Local field
Wave packet system
Wavelet frame
Gabor frame
42C40
Local field
Wave packet system
Fourier transform
11S85
42C15
Wavelet frame
43A70
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ISSN0393-0440
1879-1662
DOI10.1016/j.geomphys.2017.05.015

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Summary:In this paper, we introduce the notion of wave packet systems on local fields of positive characteristic and derive some characterizations of these systems by means of two basic equations in the Fourier domain. More precisely, we establish a complete characterization of orthogonal wave packet systems in L2(K) which include the corresponding results of wavelet analysis and Gabor theory as the special cases. We shall also provide a sufficient condition of the completeness of wave packet systems on local fields of positive characteristic subject to some mild conditions. The paper concludes with the necessary and sufficient conditions for the wave packet systems to be wave packet Parseval frames for L2(K).
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2017.05.015