Discrete orthogonal and Riesz refinable functions on local fields of positive characteristic

2020 ◽  
Vol 6 (4) ◽  
pp. 1505-1522
Author(s):  
Gleb S. Berdnikov ◽  
Sergei F. Lukomskii
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Refinable Functions ◽  
Discrete Orthogonal

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

scholarly journals Characterization of wavelets and MRA wavelets on local fields of positive characteristic

2014 ◽  
Vol 66 (1) ◽  
pp. 33-53 ◽  
Author(s):  
Biswaranjan Behera ◽  
Qaiser Jahan
Keyword(s):  
Positive Characteristic ◽  
Local Fields

scholarly journals Dualwavelet frames in Sobolev spaces on local fields of positive characteristic

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2091-2099
Author(s):  
Ishtaq Ahmad ◽  
Neyaz Sheikh
Keyword(s):  
Sobolev Spaces ◽  
Local Field ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
The Past ◽  
Dual Wavelet Frames ◽  
Dual Wavelet ◽  
Field Of Positive Characteristic

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. In this article, we obtain the characterization of nonhomogeneous wavelet frames and nonhomogeneous dual wavelet frames in a Sobolev spaces on a local field of positive characteristic by means of a pair of equations.

scholarly journals MRA on Local Fields of Positive Characteristic

2014 ◽  
Vol 14 (4) ◽  
pp. 511-518 ◽  
Author(s):  
A. M. Vodolasov ◽  
◽  
S. F. Lukomskii ◽  
Keyword(s):  
Positive Characteristic ◽  
Local Fields

scholarly journals A Short Note on Wavelet Frames Based on FMRA on Local Fields

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
M. Younus Bhat
Keyword(s):  
Multiresolution Analysis ◽  
Positive Characteristic ◽  
Minimum Energy ◽  
Short Note ◽  
Explicit Construction ◽  
Local Fields ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Frame Multiresolution Analysis ◽  
Field Of Positive Characteristic

The concept of frame multiresolution analysis (FMRA) on local fields of positive characteristic was given by Shah in his paper, Frame Multiresolution Analysis on Local Fields published by Journal of Operators. The author has studied the concept of minimum-energy wavelet frames on these prime characteristic fields. We continued the studies based on frame multiresolution analysis and minimum-energy wavelet frames on local fields of positive characteristic. In this paper, we introduce the notion of the construction of minimum-energy wavelet frames based on FMRA on local fields of positive characteristic. We provide a constructive algorithm for the existence of the minimum-energy wavelet frame on the local field of positive characteristic. An explicit construction of the frames and bases is given. In the end, we exhibit an example to illustrate our algorithm.

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