Related papers: The pseudospectrum of an operator with Bessel-type…
The indefinite Sturm-Liouville operator $A = (\sgn x)(-d^2/dx^2+q(x))$ is studied. It is proved that similarity of $A$ to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of…
We obtain sharp asymptotic formulas for the eigenvalues and norming constants of Sturm-Liouville operators associated with the differential expression \[ -\frac{d^2}{dx^2} + x + q(x), \quad x\in [0,\infty), \] together with the boundary…
Quasinormal modes and frequencies are the eigenvectors and eigenvalues of a non-Hermitian differential operator. They hold crucial significance in the physics of black holes. The analysis of quasinormal modes of black holes in…
In this paper we study spectral function for a nonsymmetric differential operator on the half line. Two cases of the coefficient matrix are considered, and for each case we prove by Marchenko's method that, to the boundary value problem,…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…
In this study, we define discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Gr\"unwald-Letnikov fractional operators with both delta and nabla operators. We show selfadjointness of the DFSL operator for the…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We describe the wave functional model for the minimal (symmetric) Sturm-Liouville operator on the finite interval. We construct the wave spectrum of this operator, then, following the abstract scheme, we construct the model space of…
We examine the spectrum of a family of Sturm--Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described in a…
We study the pseudospectrum of a class of non-selfadjoint differential operators. Our work consists in a detailed study of the microlocal properties, which rule the spectral stability or instability phenomena appearing under small…
We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic problem computed for the spectral parameter equal to $0$.…
The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class $W_2^{-1}$ is studied. This operator generalizes Sturm-Liouville operators…
The work is devoted to the study of the similarity of a correct restriction to some self-adjoint operator in the case when the minimal operator is symmetric. The resulting theorem was applied to the Sturm-Liouville operator and the Laplace…
We are concerned with the non-normal Schr\"odinger operator $$ H=-\Delta+V $$ on $ L^2(\mathbb R^n)$, where $V\in W^{1,\infty}_{\text{loc}}(\mathbb{R}^n)$ and $\operatorname{Re} (V(x))\ge c|x|^2-d$ for some $c,d>0$. The spectrum of this…
We deal with the Sturm--Liouville operator $Ly=l(y)=-\dfrac{d^2y}{dx^2}+q(x)y,$ with Dirichlet--Neumann boundary conditions $ y(0)=y'(\pi)=0 $ in the space $L_2[0,\pi]$. We assume that the potential $q$ is complex-valued and has the form…
We study the Sturm--Liouville operator $$ T(\varepsilon)y=-\frac{1}{\varepsilon}y''+ p(x)y, $$ with concrete $\mathcal{PT}$-- symmetric potential $p(x) = ix$ and Dirichlet boundary conditions on the segment $[-1,1]$. Here $\varepsilon \in…
In this work, we investigate the spectral problem $Au = {\lambda}u$ where $A$ is a fractional elliptic operator involving left- and right-sided Riemann-Liouville derivatives. These operators are nonlocal and nonsymmetric, however, share…
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…
The spectral properties of the pseudo-differential operator $(-d^2/dx^2)^{1/2}+x^2$ are analyzed by a combination of functional integration methods and direct analysis. We obtain a representation of its eigenvalues and eigenfunctions, prove…