Related papers: Trace formulas for Schr\"odinger operators with co…
This paper presents the spectral analysis of 1-dimensional Schroedinger operator on the half-line whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. The coupling constants are allowed to be…
We count invertible Schr\"odinger operators (perturbations by diagonal matrices of the adjacency matrix) over finite fieldsfor trees, cycles and complete graphs.This is achieved for trees through the definition and use of local invariants…
We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous…
We review some results and proofs on eigenvalue bounds for random Schr\"odinger operators with complex-valued potentials. We also include new Schatten norm estimates for the resolvent and use them to obtain bounds for sums of eigenvalues.
We construct non-random bounded discrete half-line Schr\" odinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse…
We study the effect of non-negative potentials on the spectral gap of one-dimensional Schr\"odinger operators in the limit of large intervals. In particular, we derive upper and lower bounds on the gap for different classes of potentials…
We develop a Fredholm alternative for a fractional elliptic operator~$\mathcal{L}$ of mixed order built on the notion of fractional gradient. This operator constitutes the nonlocal extension of the classical second order elliptic operators…
We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric…
We construct 1-dim difference Schr\"odinger operators with a class of Gevrey potentials such that Cantor spectrum occurs together with the estimations of open spectral gaps . The proof is based on KAM and Moser-P\"oschel argument .
In this paper we study unique continuation theorems for magnetic Schr\"odinger equation via Carleman estimates. We use integration by parts techniques in order to show these estimates. We consider electric and magnetic potentials with…
We consider the radial Dirac operator with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the…
A two-dimensional Schr\"odinger operator with a constant magnetic field perturbed by a smooth compactly supported potential is considered. The spectrum of this operator consists of eigenvalues which accumulate to the Landau levels. We call…
In this paper we investigate the spectrum and spectrality of the one-dimensional Schrodinger operator with a periodic PT-symmetric complex-valued potential.
Let H be a Schrodinger operator on the real line, where the potential is in L^1 and L^2. We define the perturbed Fourier transform F for H and show that F is an isometry from the absolute continuous subspace onto L^2. This property allows…
Spectral properties of Schr\"odinger operators on compact metric graphs are studied and special emphasis is put on differences in the spectral behavior between different classes of vertex conditions. We survey recent results especially for…
We consider the spectral theory for discrete Schr\"odinger operators on the hexagonal lattice and their inverse scattering problem. We give a procedure for reconstructing the compactly supported potential from the scattering matrix for all…
We study adjointable, bounded operators on the direct sum of two copies of the standard Hilbert C*-module over a unital C*-algebra A that are given by upper triangular 2 by 2 operator matrices. Using the definition of A-Fredholm and…
The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the…
We derive a sharp bound on the location of non-positive eigenvalues of Schroedinger operators on the halfline with complex-valued potentials.
In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in $R^n$ with $n \geq 3$, from measurements on open subsets of its boundary. This inverse problem is…