Related papers: Inverse resonance problems for the Schroedinger op…
In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a…
We study discrete Schroedinger operators with compactly supported potentials on the square lattice. Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely…
We prove upper bounds on the number of resonances and eigenvalues of Schr\"odinger operators $-\Delta+V$ with complex-valued potentials, where $d\geq 3$ is odd. The novel feature of our upper bounds is that they are \emph{effective}, in the…
In this paper, we study forward problem and inverse problem for the fractional magnetic Schrodinger equation with nonlinear electric potential. We first investigate the maximum principle for the linearized equation and apply it to show that…
We study the resonances of (generally, non-selfadjoint) Schr\"odinger operators with matrix-valued square-well potentials. We compute explicitly the Jost function and derive complex transcendental equations for the resonances. We prove…
This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential $q$ is known a priori on a subinterval $ \left[ b,\pi…
We obtain new results about the high-energy distribution of resonances for the one-dimensional Schr\"odinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular…
We work with the Schr\" odinger equation \begin{equation*} H_q y = -y'' + q(x)y = z^2y, \ x\in [0,\infty), \end{equation*} where $q\in L_1((0,\infty), xdx)$, and asssume that the corresponding operator $H_q$ is defined by the Dirihlet…
In this paper, we focus on the inverse scattering problem for the nonlinear Schrodinger equation with magnetic potentials. Specifically, we investigate whether the scattering operator associated with the nonlinear Schrodinger equation can…
Let $A\in\mathrm{Sym}(n\times n)$ be an elliptic 2-tensor. Consider the anisotropic fractional Schr\"odinger operator $\mathscr{L}_A^s+q$, where $\mathscr{L}_A^s:=(-\nabla\cdot(A(x)\nabla))^s$, $s\in (0, 1)$ and $q\in L^\infty$. We are…
In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be…
We study the inverse Robin problem for the Schr\"odinger equation in a half-space. The potential is assumed to be compactly supported. We first solve the direct problem for dimensions two and three. We then show that the Robin-to-Robin map…
We consider the Schr\"odinger operator $H$ with a periodic potential $p$ plus a compactly supported potential $q$ on the half-line. We prove the following results: 1) a forbidden domain for the resonances is specified, 2) asymptotics of the…
In this work, we consider the Sturm-Liouville operator on a finite interval $[0,1]$ with discontinuous conditions at $1/2$. We prove that if the potential is known a priori on a subinterval $[b,1]$ with $b\ge1/2$, then parts of two spectra…
We study the inverse problem of determining the vector and scalar potentials $\mathcal{A}(t,x)=\left(A_{0},A_{1},\cdots,A_{n}\right)$ and $q(t,x)$, respectively, in the relativistic Schr\"odinger equation \begin{equation*}…
The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants.…
This article deals with the inverse problem of determining the unbounded real-valued electric potential of the Robin Laplacian on a bounded domain of dimension 3 or greater, by incomplete knowledge of its boundary spectral data. Namely, the…
In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…
We consider the inverse problem of the determining the potential in the dynamical Schr\"odinger equation on the interval by the measurement on the whole boundary. Provided that source is \emph{generic} using the Boundary Control method we…
In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…