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Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko , Chuan-Fu Yang

In this work, we study the inverse spectral problems for the Sturm-Liouville operators on [0,1] with complex coefficients and a discontinuity at $x=a\in(0,1)$. Assume that the potential on (a,1) and some parameters in the discontinuity and…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Chuan-Fu Yang , Natalia Pavlovna Bondarenko

In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…

Spectral Theory · Mathematics 2025-06-19 Tim Binz , Jonas Lampart

This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The…

Classical Analysis and ODEs · Mathematics 2023-12-01 Nourredine Houari , Faouzi Haddouchi

We give a comprehensive treatment of Sturm-Liouville operators with measure-valued coefficients including, a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl-Titchmarsh theory. We avoid previous…

Spectral Theory · Mathematics 2013-08-14 Jonathan Eckhardt , Gerald Teschl

We prove a variant of Krein's resolvent formula expressing the resolvents of self-adjoint extensions through the associated boundary conditions. Applications to solvable quantum-mechanical problems are discussed.

Functional Analysis · Mathematics 2011-11-10 Konstantin Pankrashkin

We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green's identity for the nonlocal operator that recovers the classical boundary integral,…

Analysis of PDEs · Mathematics 2023-08-11 James M. Scott , Qiang Du

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…

Functional Analysis · Mathematics 2014-07-17 Eugenia N. Petropoulou , L. Velázquez

In this study we are concerned with a class of generalized BVP' s consisting of eigendependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical…

Classical Analysis and ODEs · Mathematics 2013-04-17 Kadriye Aydemir

A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace-Beltrami operator on manifolds with boundary in any dimension is presented. The algorithm is based on the characterisation of a large…

Numerical Analysis · Mathematics 2017-08-23 A. López-Yela , J. M. Pérez-Pardo

We suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…

Spectral Theory · Mathematics 2023-04-13 Sergey Buterin , Sergey Vasilev

This note supplements the work of Gomez-Ullate, Kamran and Milson on the X_(1)-Jacobi polynomials which are orthogonal in a weighted Hilbert function space on the the interval (-1,+1) of the real line. These polynomials are generated by a…

Classical Analysis and ODEs · Mathematics 2008-12-04 W. N. Everitt

We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and…

Spectral Theory · Mathematics 2015-02-02 Oleg Gorbunov , Vjacheslav Yurko

In this work, firstly in the Hilbert space of vector-functions L^2 (H,(-\infty,a)\bup(b,+\infty)),a<b all selfadjoint extensions of the minimal operator generated by linear singular symmetric differential expression l(\cdot)=i d/dt+A with a…

Functional Analysis · Mathematics 2011-05-27 E. Bairamov , R. O. Mert , Z. I. Ismailov

The present work devoted to the finding explicit solution of a boundary problem with the Dirichlet-Neumann condition for elliptic equation with singular coefficients in a quarter of ball. For this aim the method of Green's function have…

Analysis of PDEs · Mathematics 2015-12-08 M. S. Salakhitdinov , E. T. Karimov

In this note we provide estimates for the lower bound of the self-adjoint operator associated with the three-coefficient Sturm-Liouville differential expression $$ \frac{1}{r} \left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm…

Spectral Theory · Mathematics 2022-12-21 Jussi Behrndt , Fritz Gesztesy , Philipp Schmitz , Carsten Trunk

For a singular oscillator, the Schrodinger equation is obtained an equation of eigenvalues, and the dependence of energy on the self-adjoint extension parameter is established. It is shown that the self-adjoint extension violates the…

Quantum Physics · Physics 2024-06-21 Anzor Khelashvili , Teimuraz Nadareishvili

Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and $V$ be a compact non-selfadjoint perturbation. We relate the regularity properties of $V$ to various spectral…

Spectral Theory · Mathematics 2020-05-22 Olivier Bourget , Diomba Sambou , Amal Taarabt

The paper deals with singular Sturm-Liouville expressions with matrix-valued distributional coefficients. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent…

Functional Analysis · Mathematics 2016-12-14 Alexei Konstantinov , Oleksandr Konstantinov

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

Classical Analysis and ODEs · Mathematics 2012-05-11 Yu. A. Konyaev