Related papers: Lieb-Thirring estimates for non self-adjoint Schr\…

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity…

We consider the inverse problem of determining the time dependent magnetic field of the Schr\"odinger equation in a bounded open subset of $R^n$, with $n \geq 1$, from a finite number of Neumann data, when the boundary measurement is taken…

We study the spectra of non-selfadjoint first-order operators on the interval with non-local point interactions, formally given by ${i\partial_x+V+k\langle \delta,\cdot\rangle}$. We give precise estimates on the location of the eigenvalues…

The symmetric Al-Salam--Chihara polynomials for $q>1$ are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on $\ell^2(\Z)$ to which these polynomials are eigenfunctions. We determine…

We define functions of noncommuting self-adjoint operators with the help of double operator integrals. We are studying the problem to find conditions on a function $f$ on ${\Bbb R}^2$, for which the map $(A,B)\mapsto f(A,B)$ is Lipschitz in…

We investigate $L^1(\mathbb R^n)\to L^\infty(\mathbb R^n)$ dispersive estimates for the Schr\"odinger operator $H=-\Delta+V$ when there is an eigenvalue at zero energy and $n\geq 5$ is odd. In particular, we show that if there is an…

In this paper we approximate a Schr\"odinger operator on $L^2(\R)$ by Jacobi operators on $\ell^2(\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\gamma=1/2$ and $\gamma=3/2$. To this end we first investigate…

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 construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation…

Let $f: \mathbb{R}^d \to\mathbb{R}$ be a Lipschitz function. If $B$ is a bounded self-adjoint operator and if $\{A_k\}_{k=1}^d$ are commuting bounded self-adjoint operators such that $[A_k,B]\in L_1(H),$ then…

The eigenvalues of a self-adjoint nxn matrix A can be put into a decreasing sequence $\lambda=(\lambda_1,...,\lambda_n)$, with repetitions according to multiplicity, and the diagonal of A is a point of $R^n$ that bears some relation to…

This paper investigates the $L^p$-boundedness of wave operators associated with the nonhomogeneous fourth-order Sch\"odinger operator $H = \Delta^2 - \Delta + V(x)$ on $\mathbb{R}^n$. Assuming the real-valued potential $ V $ exhibits…

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…

This article studies the pointwise convergence for the fractional Schr\"odinger operator $P^{t}_{a,\gamma}$ with complex time in one spatial dimension. Through establishing $L^2$-maximal estimates for initial datum in $H^{s}(\mathbb{R})$,…

In $L_2 (\mathbb{R}^d; \mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\mathcal{A}_\varepsilon$ with periodic coefficients depending on $\mathbf{x}/\varepsilon$. We find approximations…

We prove necessary and sufficient conditions for the Schr\"odinger operators to have zero-energy bound states at the threshold of the essential spectrum such that they have bounded $k$-th moment. This result is the extension of the results…

Inequalities are derived for sums and quotients of eigenvalues of magnetic Schroedinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.

We prove a Lieb--Thirring inequality for Schr\"odinger operators $-\frac{\mathrm{d}^2}{\mathrm{d}x^2}+V$ on the semi-axis with Robin boundary condition at the origin. The result improves on a bound obtained by P.~Exner, A.~Laptev and…

We work in the setting of infinite, not necessarily locally finite, weighted graphs. We give a sufficient condition for the essential self-adjointness of (discrete) Schr\"odinger operators $\mathcal{L}_{V}$ that are not necessarily lower…

We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schr\"odinger operators, the asymptotic repartition of eigenvectors is the same as in the regular…