Related papers: Carleman estimates and absence of embedded eigenva…

We investigate the persistance of embedded eigenvalues under perturbations of a certain self-adjoint Schr\"odinger-type differential operator in $L^2(\mathbb{R};\mathbb{R}^n)$, with an asymptotically periodic potential. The studied…

We prove a dispersive estimate for the evolution of Schroedinger operators $H = -\Delta + V(x)$ in ${\mathbb R}^3$. The potential is allowed to be a complex-valued function belonging to $L^p(\R^3)\cap L^q(\R^3)$, $p < \frac32 < q$, so that…

We study eigenvalues of non-self-adjoint Schr\"odinger operators on non-trapping asymptotically conic manifolds of dimension $n\ge 3$. Specifically, we are concerned with the following two types of estimates. The first one deals with Keller…

This note aims to give prominence to some new results on the absence and localization of eigenvalues for the Dirac and Klein-Gordon operators, starting from known resolvent estimates already established in the literature combined with the…

Building on the work of Jitomirskaya-Simon and Jitomirskaya-Liu, who established the absence of eigenvalues for Schr\"odinger operators with almost reflective repetition potentials, we provide a new proof of the sharp Gordon's lemma, which…

Using a correspondence between the spectrum of the damped wave equation and non-self-adjoint Schroedinger operators, we derive various bounds on complex eigenvalues of the former. In particular, we establish a sharp result that the…

Assuming the negative part of the potential is uniformly locally $L^1$, we prove a pointwise $L^p$ estimate on derivatives of eigenfunctions of one-dimensional Schrodinger operators. In particular, if an eigenfunction is in $L^p$, then so…

We investigate the persistence of embedded eigenvalues for a class of magnetic Laplacians on an infinite cylindrical domain. The magnetic potential is assumed to be $C^2$ and asymptotically periodic along the unbounded direction, with an…

We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian.

An explicit construction is provided for embedding n positive eigenvalues in the spectrum of a Schroedinger operator on the half-line with a Dirichlet boundary condition at the origin. The resulting potential is of von Neumann-Wigner type,…

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…

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a…

In this work we prove that the eigenvalues of the $n$-dimensional massive Dirac operator $\mathscr{D}_0 + V$, $n\ge2$, perturbed by a possibly non-Hermitian potential $V$, are localized in the union of two disjoint disks of the complex…

We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.

In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension~$n\geq 2$. We use them to derive Cwikel-Lieb-Rozenblum inequalities and and Lieb-Thirring inequalities for the number of negative eigenvalues of…

By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point spectrum. The settings…

In this paper, we study eigenvalues of the closed eigenvalue problem of the differential operator $ L$, which is introduced by Colding and Minicozzi in [4], on an $n$-dimensional compact self-shrinker in ${R}^{n+p}$. Estimates for…

The celebrated Cwikel-Lieb_Rozenblum inequality gives an upper estimate for the number of negative eigenvalues of Schroedinger operators in dimension three and higher. The situation is much more difficult in the two dimensional case. There…

In this paper, we give Lieb-Thirring type inequalities for isolated eigenvalues of $d$-dimensional non-selfadjoint Schr\"{o}dinger operators with complex-valued and dilation analytic potentials. In order to derive them, we prove that…

A virial theorem is established for the operator proposed by Brown and Ravenhall as a model for relativistic one-electron atoms. As a consequence, it is proved that the operator has no eigenvalues greater than $\max(m c^2, 2 \alpha Z -…