Related papers: Iso-bispectral potentials for Sturm-Liouville-type…
In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace…
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…
In this work, we study inverse resonance problems for the Schr\"odinger operator on the real line with the potential supported in $[0,1]$. In general, all eigenvalues and resonances can not uniquely determine the potential. (i) It is shown…
This paper starts a series devoted to the vector-valued Sturm-Liouville problem $-\psi''+V(x)\psi=\lambda\psi$, $\psi\in L^2([0,1];\mathbb{C}^N)$, with separated boundary conditions. The overall goal of the series is to give a complete…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
We describe the necessary and sufficient conditions for two sequences {\mu_n}^\infty_n=0 and {a_n}^\infty_n=0 to be correspondingly the set of eigenvalues and the set of norming constants of a Sturm-Liouville problem with real summable…
The necessary and sufficient conditions are found for the two sequences $\left\{\mu_n \right\}_{n=0}^{\infty}$ and $\left\{a_n \right\}_{n=0}^{\infty}$ to be the spectrum and the norming constants respectively, for a boundary value problem…
In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…
We formulate the inverse spectral theory for a non-self-adjoint one-dimensional Dirac operator associated periodic potentials via a Riemann-Hilbert problem approach. We use the resulting formalism to solve the initial value problem for the…
The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…
We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints. For general boundary conditions we obtain refined and new results about their…
We consider difference operators in $L^2$ on $\R$ of the form $$ L f(s)=p(s)f(s+i)+q(s) f(s)+r(s) f(s-i) ,$$ where $i$ is the imaginary unit. The domain of definiteness are functions holomorphic in a strip with some conditions of decreasing…
In this paper we consider the Sturm-Liouville equation -y"+qy = lambda*y on the half line (0,infinity) under the assumptions that x=0 is a regular singular point and nonoscillatory for all real lambda, and that either (i) q is L_1 near…
We consider the spectral function $\rho(\mu)$ $(\mu \geq 0)$ for the Sturm-Liouville equation $y^{''}+(\lambda-q)y =0$ on $[0,\infty)$ with the boundary condition $y(0)=0$ and where $q$ has slow decay $O(x^{-\alpha})$ $(a>0)$ as $x\to…
In this paper, we consider a wave equation on a bounded domain with a Sturm-Liouville operator with a singular intermediate coefficient and a singular potential. To obtain and evaluate the solution, the method of separation of variables is…
Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm…
We investigate the spectral properties of the maximal operator $A$ associated with a differential expression $\frac 1 w(-\frac d {dx}(p\frac d {dx}) + q)$ with real-valued periodic coefficients $w$, $p$ and $q$ where $w$ changes sign. It…
In this study, a formula for regularized sums of eigenvalues of a Sturm-Liouville problem with retarded argument at the point of discontinuity is obtained. Moreover, oscillation properties of the related problem is investigated.
An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horv\'ath and Apagyi [Mod. Phys. Lett. B 22, 2137 (2008)] is examined in various aspects and developed further to (re)construct…
In this paper we study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from two spectra. We give a reconstruction algorithm and establish existence and uniqueness of reconstruction. Our approach…