A characterization of potential kernels on the positive half-line

1978 ◽  
Vol 41 (4) ◽  
pp. 335-340 ◽  
Author(s):  
Gunnar Forst
Keyword(s):  
Half Line ◽  
Positive Half

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.

WAVELET PACKETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF LINE

2013 ◽  
Vol 06 (01) ◽  
pp. 1350007 ◽  
Author(s):  
Vikram Sharma ◽  
P. Manchanda
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packets ◽  
Half Line ◽  
State University ◽  
Spectral Pairs ◽  
Funct Anal ◽  
Positive Half

Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform multiresolution analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied multiresolution analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform multiresolution analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.

scholarly journals A characterization of singular Schrödinger operators on the half-line

2020 ◽  
pp. 1-19
Author(s):  
Raffaele Scandone ◽  
Lorenzo Luperi Baglini ◽  
Kyrylo Simonov
Keyword(s):  
Schrödinger Operators ◽  
Half Line ◽  
Schrodinger Operators

scholarly journals Asymptotic solution of Sturm-Liouville problem with periodic boundary conditions for relativistic finite-difference Schrödinger equation

2020 ◽  
Vol 28 (3) ◽  
pp. 230-251
Author(s):  
Ilkizar V. Amirkhanov ◽  
Irina S. Kolosova ◽  
Sergey A. Vasilyev
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Asymptotic Series ◽  
Periodic Boundary Conditions ◽  
Singularly Perturbed ◽  
Half Line ◽  
Asymptotic Convergence ◽  
Relativistic Particles ◽  
Positive Half

The quasi-potential approach is very famous in modern relativistic particles physics. This approach is based on the so-called covariant single-time formulation of quantum field theory in which the dynamics of fields and particles is described on a space-like three-dimensional hypersurface in the Minkowski space. Special attention in this approach is paid to methods for constructing various quasi-potentials. The quasipotentials allow to describe the characteristics of relativistic particles interactions in quark models such as amplitudes of hadron elastic scatterings, mass spectra, widths of meson decays and cross sections of deep inelastic scatterings of leptons on hadrons. In this paper SturmLiouville problems with periodic boundary conditions on a segment and a positive half-line for the 2m-order truncated relativistic finite-difference Schrdinger equation (LogunovTavkhelidzeKadyshevsky equation, LTKT-equation) with a small parameter are considered. A method for constructing of asymptotic eigenfunctions and eigenvalues in the form of asymptotic series for singularly perturbed SturmLiouville problems with periodic boundary conditions is proposed. It is assumed that eigenfunctions have regular and boundary-layer components. This method is a generalization of asymptotic methods that were proposed in the works of A. N. Tikhonov, A. B. Vasilyeva, and V. F Butuzov. We present proof of theorems that can be used to evaluate the asymptotic convergence for singularly perturbed problems solutions to solutions of degenerate problems when 0 and the asymptotic convergence of truncation equation solutions in the case m. In addition, the SturmLiouville problem on the positive half-line with a periodic boundary conditions for the quantum harmonic oscillator is considered. Eigenfunctions and eigenvalues are constructed for this problem as asymptotic solutions for 4-order LTKT-equation.

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