Related papers: Eigenvalue estimates for Schroedinger operators on…
We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schroedinger-like operators remain true, with possibly different constants, when the critical Hardy-weight $C|x|^{-2}$ is subtracted from the Laplace…
We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schr\"odinger operator $-\Delta - (d-2)^2/(4|x|^2) -W(x)$ on $L^2(\mathbb{R}^d)$. The bound is given in terms of a weighted $L^{d/2}-$norm…
We consider a Schr\"odinger operator on the half-line with a Dirichlet boundary condition at the origin and show that moments of its negative eigenvalues can be estimated by the part of the potential that is larger than the critical Hardy…
For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and…
We study the discreteness of the spectrum of Schrodinger operators which are defined on N-dimensional rooted trees of a finite or infinite volume, and are subject to a certain mixed boundary condition. We present a method to estimate their…
We prove upper and lower bounds for the number of eigenvalues of semi-bounded Schr\"odinger operators in all spatial dimensions. As a corollary, we obtain two-sided estimates for the sum of the negative eigenvalues of atomic Hamiltonians…
We derive a sharp bound on the location of non-positive eigenvalues of Schroedinger operators on the halfline with complex-valued potentials.
Given a Schr\"odinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The…
We prove conditions on potentials which imply that the sum of the negative eigenvalues of the Schroeodinger operator is finite. We use a method for bounding eigenvalues based on estimates of the Hilbert-Schmidt norm of semigroup differences…
This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schroedinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L^1 norms and L ln L norms of the…
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…
We investigate the spectrum of Schr\"odinger operators on finite regular metric trees through a relation to orthogonal polynomials that provides a graphical perspective. As the Robin vertex parameter tends to $-\infty$, a narrow cluster of…
We prove an analogue for trees of Courant's theorem on the interlacing property of zeros of eigenfunctions of a Schr\"{o}dinger operator. Let $\Gamma$ be a finite tree, and $\mathcal A$ a Schr\"{o}dinger operator on $\Gamma$. If the…
It is well-known that for usual Schroedinger operators weakly coupled bound states exist in dimensions one and two, whereas in higher dimensions the famous Cwikel-Lieb-Rozenblum bound holds. We show for a large class of Schr\"odinger-type…
Consider the Schr\"odinger operators $H_{\pm}=-d^2/dx^2\pm V(x)$. We present a method for estimating the potential in terms of the negative eigenvalues of these operators. Among the applications are inverse Lieb-Thirring inequalities and…
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider,…
We consider a Sturm-Liouville operator a with integrable potential $q$ on the unit interval $I=[0,1]$. We consider a Schr\"odinger operator with a real compactly supported potential on the half line and on the line, where this potential…
We obtain bounds on the complex eigenvalues of non-self-adjoint Schr\"odinger operators with complex potentials, and also on the complex resonances of self-adjoint Schr\"odinger operators. Our bounds are compared with numerical results, and…
Consider a regular $d$-dimensional metric tree $\Gamma$ with root $o$. Define the Schroedinger operator $-\Delta - V$, where $V$ is a non-negative, symmetric potential, on $\Gamma$, with Neumann boundary conditions at $o$. Provided that $V$…
Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover…