scholarly journals Orthogonal Gabor systems on local fields

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5193-5201
Author(s):  
Firdous Shah ◽  
Owais Ahmad ◽  
Neyaz Sheikh
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Tight Frames ◽  
Fourier Domain ◽  
Gabor Systems ◽  
Orthonormal Bases ◽  
Basic Equations

The objective of this paper is to provide complete characterizations of orthogonal families, tight frames and orthonormal bases of Gabor systems on local fields of positive characteristic by means of some basic equations in the Fourier domain.

Semi-orthogonal wavelet frames on local fields

Analysis ◽  
2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Firdous A. Shah ◽  
M. Younus Bhat
Keyword(s):  
Finite Number ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
Orthogonal Wavelet ◽  
Basic Equations ◽  
Frame Multiresolution Analysis ◽  
Frame Wavelets ◽  
Equivalent Conditions

AbstractWe investigate semi-orthogonal wavelet frames on local fields of positive characteristic and provide a characterization of frame wavelets by means of some basic equations in the frequency domain. The theory of frame multiresolution analysis recently proposed by Shah [J. Operators (2015), Article ID 216060] on local fields is used to establish equivalent conditions for a finite number of functions

scholarly journals Gabor systems on positive half line via Walsh-Fourier transform

2020 ◽  
Vol 12 (2) ◽  
pp. 468-482
Author(s):  
O. Ahmad ◽  
N.A. Sheikh
Keyword(s):  
Fourier Transform ◽  
Applied Mathematics ◽  
Vital Role ◽  
Complete Characterization ◽  
Half Line ◽  
Tight Frames ◽  
Gabor Systems ◽  
Orthonormal Bases ◽  
Positive Half

Gabor systems play a vital role not only in modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this paper, we investigate Gabor systems on positive half line via Walsh-Fourier transform. We provide the complete characterization of orthogonal Gabor systems on positive half line. Furthermore, we provide the characterization of tight frames and orthonormal bases of Gabor systems on positive half line in Fourier domain.

Characterization of Low-pass Filters on Local Fields of Positive Characteristic

2016 ◽  
Vol 59 (3) ◽  
pp. 528-541 ◽  
Author(s):  
Qaiser Jahan
Keyword(s):  
Positive Characteristic ◽  
Sufficient Conditions ◽  
Local Fields ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Necessary And Sufficient ◽  
Low Pass Filters ◽  
The Scaling Function

AbstractIn this article, we give necessary and sufficient conditions on a function to be a low-pass filter on a local field K of positive characteristic associated with the scaling function for multiresolution analysis of L2(K). We use probability and martingale methods to provide such a characterization.

scholarly journals How to construct wavelets on local fields of positive characteristic

2017 ◽  
Vol 38 (4) ◽  
pp. 615-621
Author(s):  
G. Berdnikov ◽  
Iu. Kruss ◽  
S. Lukomskii
Keyword(s):  
Positive Characteristic ◽  
Local Fields
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