Periodic Wavelet Frames on Local Fields of Positive Characteristic

2016 ◽  
Vol 37 (5) ◽  
pp. 603-627 ◽  
Author(s):  
Firdous A. Shah
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
Periodic Wavelet ◽  
Periodic Wavelet Frames

The Study of Tight Periodic Wavelet Frames and Wavelet Frame Packets and Applications

2014 ◽  
Vol 977 ◽  
pp. 532-535
Author(s):  
Qing Jiang Chen ◽  
Yu Zhou Chai ◽  
Chuan Li Cai
Keyword(s):  
Information Science ◽  
Approximation Order ◽  
Tight Frame ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Periodic Wavelet ◽  
Unitary Extension ◽  
Periodic Wavelet Frames ◽  
Necessary And Sufficient

Information science focuses on understanding problems from the perspective of the stake holders involved and then applying information and other technologies as needed. A necessary and sufficient condition is identified in term of refinement masks for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approxi-mation order of truncated tight frame series is established, which facilitates construction of tight periodic wavelet frames with desirable approximation order. The pyramid decomposition scheme is derived based on the generalized multiresolution structure.

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 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.

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 Polyphase matrix characterization of framelets on local fields of positive characteristic

2017 ◽  
Vol 9 (1) ◽  
pp. 248-259
Author(s):  
F. A. Shah ◽  
M. Y. Bhat
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension ◽  
Polyphase Matrix

AbstractAn important tool for the construction of framelets on local fields of positive characteristic using unitary extension principle was presented by Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307]. In this article, we continue the study of framelets on local fields and present a polyphase matrix characterization of framelets generated by the extension principle.

scholarly journals Frame Multiresolution Analysis on Local Fields of Positive Characteristic

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Firdous A. Shah
Keyword(s):  
Multiresolution Analysis ◽  
Positive Characteristic ◽  
Scaling Function ◽  
Local Fields ◽  
Wavelet Frames ◽  
Shift Invariant Spaces ◽  
Frame Multiresolution Analysis ◽  
Invariant Spaces ◽  
The Scaling Function

We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspace V0 of L2(K) has a frame, a collection of translates of the scaling function φ of the form φ(·-u(k)):k∈N0, where N0 is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field K of positive characteristic using the shift-invariant space theory.

On construction of periodic wavelet frames

2018 ◽  
Vol 5 (1) ◽  
pp. 241-249
Author(s):  
Pavel Andrianov ◽  
Maria Skopina
Keyword(s):  
Wavelet Frames ◽  
Periodic Wavelet ◽  
Periodic Wavelet Frames
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