Related papers: Spectral inequalities for Schroedinger operators w…
We prove upper and lower bounds for sums of eigenvalues of Lieb-Thirring type for non-self-adjoint Schr\"odinger operators on the half-line. The upper bounds are established for general classes of integrable potentials and are shown to be…
Positivity, essential self-adjointness, and spectral properties of a class of Schroedinger operators with multipolar inverse-square potentials are discussed. In particular a necessary and sufficient condition on the masses of singularities…
This paper is essentially derived from the observation that some results used for improving constants in the Lieb-Thirring inequalities for Schrodinger operators in L2(-\infty,\infty) can be translated to the discrete Schrodinger op-…
We prove that the wave operators for Schr\"odinger operators with multi-center local point interactions are the scaling limits of the ones for Schr\"odinger operators with regular potentials. We simultaneously present a proof of the…
In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson--Landau-type inequalities and to magnetic Schrodinger operators. We also obtain…
We prove optimal spectral inequalities for Landau operators in full space and in arbitrary dimension. Spectral inequalities are lower bounds on the L 2 -mass of functions in spectral subspaces of finite energy when integrated over a…
In this paper we obtain some operator versions of Levin-Steckin integral inequality.
We prove magnetic interpolation inequalities and Keller-Lieb-Thir-ring estimates for the principal eigenvalue of magnetic Schr{\"o}dinger operators. We establish explicit upper and lower bounds for the best constants and show by numerical…
In this paper we investigate the spectrum and spectrality of the one-dimensional Schrodinger operator with a periodic PT-symmetric complex-valued potential.
We prove L^1 --> L^\infty estimates for linear Schroedinger equations in dimensions one and three. The potentials are only required to satisfy some mild decay assumptions. No regularity on the potentials is assumed.
We prove $L^p$ and smoothing estimates for the resolvent of magnetic Schr\"odinger operators. We allow electromagnetic potentials that are small perturbations of a smooth, but possibly unbounded background potential. As an application, we…
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…
In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schr\"odinger operators with non-negative bounded potentials and subject to Neumann boundary conditions.
We establish the kernel estimates for the Littlewood-Paley projections associated with a Schr\"odinger operator H=-\Delta+V in \mathbb{R}^3 for a large class of short-range potentials V(x). As a corollary, we prove the homogeneous Sobolev…
This note points out some bounds for the number of negative eigenvalues of Schroedinger operators with Hardy-type potentials, which follow from a simple coordinate transformation, and could prove useful in a spectral analysis of certain…
Self-adjoint Schr\"odinger operators with $\delta$ and $\delta'$-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity…
We make a spectral analysis of discrete Schroedinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal spectral enclosures are obtained for summable potentials.…
In this paper, we establish a good-$\lz$ inequality with two parameters in the Schr\"odinger settings. As it's applications, we obtain weighted estimates for spectral multipliers and Littlewood-Paley operators and their commutators in the…
We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.
We investigate Schr\"odinger operators with \delta- and \delta'-interactions supported on hypersurfaces, which separate the Euclidean space into finitely many bounded and unbounded Lipschitz domains. It turns out that the combinatorial…