Gabor Frames on Local Fields of Positive Characteristic

Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply that the Gabor systems are Gabor frames is among the core problems in time-frequency analysis. In this paper, we give some simple and sufficient conditions that ensure a Gabor system ${M_{u(m)b}T_{u(n)a}g:m,n\in \mathbb N_{0}}$ to be a frame for L^2(K). The conditions proposed are stated in terms of the Fourier transforms of the Gabor system's generating functions.Comment: 11. arXiv admin note: text overlap with arXiv:1312.0443, arXiv:1103.0090 by other author

SUFFICIENT CONDITIONS FOR NONUNIFORM WAVELET FRAMES ON LOCAL FIELDS

The main objective of this paper is to establish a set of sufficient conditions for nonuniform wavelet frames on local fields of positive characteristic. The conditions proposed are stated in terms of the Fourier transforms of the wavelet system’s generating functions

Numerical solution of singularly perturbed problems using Haar wavelet collocation method

Abstract: In this paper, a collocation method based on Haar wavelets is proposed for the numerical solutions of singularly perturbed boundary value problems. The properties of the Haar wavelet expansions together with operational matrix of integration are utilized to convert the problems into systems of algebraic equations with unknown coefficients. To demonstrate the effectiveness and efficiency of the method various benchmark problems are implemented and the comparisons are given with other methods existing in the recent literature. The demonstrated results confirm that the proposed method is considerably efficient, accurate, simple, and computationally attractive