Results 21 to 30 of about 15,725 (152)

Spectral analysis of the truncated Hilbert transform with overlap [PDF]

, 2013
We study a restriction of the Hilbert transform as an operator $H_T$ from $L^2(a_2,a_4)$ to $L^2(a_1,a_3)$ for real numbers $a_1 < a_2 < a_3 < a_4$. The operator $H_T$ arises in tomographic reconstruction from limited data, more precisely in the method ...
Al-Aifari, Reema, Katsevich, Alexander
core   +3 more sources

A Study of the Eigenfunctions of the Singular Sturm–Liouville Problem Using the Analytical Method and the Decomposition Technique

Mathematics, 2020
The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov.
Oktay Sh. Mukhtarov, Merve Yücel
doaj   +1 more source

Inverse Sturm-Liouville problem with analytical functions in the boundary condition

Open Mathematics, 2020
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions.
Bondarenko Natalia Pavlovna
doaj   +1 more source

Squeezed States and Helmholtz Spectra [PDF]

, 1997
The 'classical interpretation' of the wave function psi(x) reveals an interesting operational aspect of the Helmholtz spectra. It is shown that the traditional Sturm-Liouville problem contains the simplest key to predict the squeezing effect for charged ...
Ammann, Ansari, Avron, Bender, Bogdan Mielnik, Brown, Brown, Delgado, Dodonov, Dodonov, Dodonov, Fernández C., Fernández C., Francisco Delgado C., Ge, Gilmore, Goyal, Hochstadt, Lindbloom, Ma, Malkin, Malkin, Marco A. Reyes, Mielnik, Mielnik, Mielnik, Poyatos, Prüfer, Rauch-Wojciechowski, Wolf, Wolf, Yuen, Zhang   +32 more
core   +2 more sources

The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems

Boundary Value Problems, 2021
In this paper, we are concerned with the eigenvalue gap and eigenvalue ratio of the Dirichlet conformable fractional Sturm–Liouville problems. We show that this kind of differential equation satisfies the Sturm–Liouville property by the Prüfer ...
Yan-Hsiou Cheng
doaj   +1 more source

INVESTIGATION OF STURM-LIOUVILLE PROBLEM SOLVABILITY IN THE PROCESS OF ASYMPTOTIC SERIES CREATION [PDF]

Научно-технический вестник информационных технологий, механики и оптики, 2015
Subject of Research. Creation of asymptotic expansions for solutions of partial differential equations with small parameter reduces, usually, to consequent solving of the Sturm-Liouville problems chain.
A. I. Popov
doaj   +1 more source

Inverse spectral problems for energy-dependent Sturm-Liouville equations

, 2012
We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants.
Ablowitz M J, Adamjan V, Albeverio S, Albeverio S, Albeverio S, Engel K-J, Gasymov M G, Gasymov M G, Gel'fand I, Gohberg I, Gohberg I C, Gusei˘nov G S, Gusei˘nov I M, Hryniv R O, Hryniv R O, Jaulent M, Jaulent M, Jaulent M, Jonas P, Kamimura Y, Kappeler T, Kato T, Levitan B M, Maksudov F G, Maksudov F G, Markus A S, Nabiev A A, Nabiev A A, Nabiev I M, Nabiev I M, Nataliya Pronska, Pronska N, Pronska N, Pronska N, Riesz F, Rostyslav Hryniv, Sattinger D H, Savchuk A M, Savchuk A M, Savchuk A M, Savchuk A M, Serier F, Yamamoto M   +42 more
core   +1 more source

Riesz Bases of Root Vectors of Indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I [PDF]

, 2007
We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter.
Binding, Paul, Ćurgus, Branko
core   +5 more sources

Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line

, 1994
The one-dimensional harmonic oscillator wave functions are solutions to a Sturm-Liouville problem posed on the whole real line. This problem generates the Hermite polynomials.
Askey R., Bender C. M., Carl M. Bender, Joshua Feinberg   +3 more
core   +1 more source

Effect of Field Line Torsion on the Polarization of ULF Waves

Journal of Geophysical Research: Space Physics, Volume 131, Issue 5, May 2026.
Abstract In this paper we suggest a simple modification of the dipole magnetic field which introduces field‐aligned currents and torsion to the field lines. The resulting field lines are not contained in the meridional planes and have resemblance to the geomagnetic field lines in the dawn and dusk flanks of the magnetosphere. We analyze polarization of
K. Kabin, A. W. Degeling, R. Rankin
wiley   +1 more source