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Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…

Spectral Theory · Mathematics 2015-02-02 Vjacheslav Yurko

We work out the perturbative expansion of quantum Liouville theory on the pseudosphere starting from the semiclassical limit of a background generated by heavy charges. By solving perturbatively the Riemann-Hilbert problem for the Poincare'…

High Energy Physics - Theory · Physics 2009-11-11 Pietro Menotti , Erik Tonni

The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…

Spectral Theory · Mathematics 2011-11-15 Natalia Bondarenko

We study the behavior of the limit of the spectrum of a non self-adjoint Sturm-Liouville operator with analytic potential as the semi-classical parameter $h\to 0$. We get a good description of the spectrum and limit spectrum near $\infty$.…

Spectral Theory · Mathematics 2007-05-23 Nedelec Laurence

In the paper, we study the problem of recovering the potential from the spectrum of the Dirichlet boundary value problem for a Sturm--Liouville equation with frozen argument on a closed set. We consider the case when the closed set consists…

Spectral Theory · Mathematics 2024-04-12 Maria Kuznetsova

We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori…

Numerical Analysis · Mathematics 2009-09-29 Norbert Roehrl

We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in…

Spectral Theory · Mathematics 2011-01-27 I. Karabash , C. Trunk

In the previous papers \cite{HLWZ,KWZ}, the jump phenomena of the $j$-th eigenvalue were completely characterized for Sturm-Liouville problems. In this paper, we show that the jump number of these eigenvalue branches is exactly the Maslov…

Functional Analysis · Mathematics 2019-03-20 Xijun Hu , Lei Liu , Li Wu , Hao Zhu

In this paper, we study spectral problems for the Sturm-Liouville operator with arbitrary complexvalued potential q(x) and two-point boundary conditions. All types of mentioned boundary conditions are considered. We ivestigate in detail the…

Spectral Theory · Mathematics 2015-12-22 Alexander Makin

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that has fixed sign (only) in a neighborhood of the boundary. We…

Analysis of PDEs · Mathematics 2021-04-05 Houssem Haddar , Shixu Meng

This article is devoted to the regular fractional Sturm--Liouville eigenvalue problem. Applying methods of fractional variational analysis we prove existence of countable set of orthogonal solutions and corresponding eigenvalues. Moreover,…

Optimization and Control · Mathematics 2014-06-04 Malgorzata Klimek , Tatiana Odzijewicz , Agnieszka B. Malinowska

We study the optimal partitioning of a (possibly unbounded) interval of the real line into $n$ subintervals in order to minimize the maximum of certain set-functions, under rather general assumptions such as continuity, monotonicity, and a…

Optimization and Control · Mathematics 2019-05-08 Paolo Tilli , Davide Zucco

We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$, parts of…

Spectral Theory · Mathematics 2016-09-13 O. P. Boyko , O. M. Martynyuk , V. N. Pivovarchik

Consider two inverse problems for Sturm-Liouville problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is…

Mathematical Physics · Physics 2023-01-13 Evgeny Korotyaev

The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient…

Spectral Theory · Mathematics 2020-09-08 Natalia P. Bondarenko

This research was devoted to investigate the inverse spectral problem of Sturm-Liouville operator with many frozen arguments. Under some assumptions, the authors obtained uniqueness theorems. At the end, a numerical simulation for the…

Spectral Theory · Mathematics 2024-07-23 Chung-Tsun Shieh , Tzong-Mo Tsai

We prove an old conjecture that relates the existence of non-real eigenvalues of Sturm-Liouville Dirichlet problems on a finite interval to the non-existence of oscillation numbers of its real eigenfunctions, [[6], p.104, Problems 3 and 5].…

Classical Analysis and ODEs · Mathematics 2024-05-01 Angelo B. Mingarelli

The classical Morse index theorem establishes a fundamental connection between the Morse index-the number of negative eigenvalues that characterize key spectral properties of linear self-adjoint differential operators-and the count of…

Dynamical Systems · Mathematics 2025-04-08 Ran Yang , Qin Xing

This paper presents a systematic study for analytic aspects of discrete spectra methods for convolution of functions supported on disks, according to the Sturm-Liouville theory. We then investigate different aspects of the presented theory…

Functional Analysis · Mathematics 2024-12-20 Arash Ghaani Farashahi , Gregory S. Chirikjian

We study conformal mappings from the unit disk to circular-arc quadrilaterals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the…

Complex Variables · Mathematics 2024-10-15 Vladislav V. Kravchenko , R. Michael Porter