Related papers: Another Application of Dilation Analytic Method fo…

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on…

We study Schr\"odinger operators $H:= -\Delta + V$ with potentials $V$ that have power-law growth (not necessarily polynomial) at 0 and at $\infty$ using methods of Lie theory (Lie-Rinehart algebras) and microlocal analysis. More precisely,…

Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and $V$ be a compact non-selfadjoint perturbation. We relate the regularity properties of $V$ to various spectral…

In this paper we are interested in generalizing Keller-type eigenvalue estimates for the non-selfadjoint Schr\"{o}dinger operator to the Dirac operator, imposing some suitable rigidity conditions on the matricial structure of the potential,…

We consider the non-selfadjoint operator [\cH = [{array}{cc} -\Delta + \mu-V_1 & -V_2 V_2 & \Delta - \mu + V_1 {array}]] where $\mu>0$ and $V_1,V_2$ are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS…

We prove a Lieb-Thirring type inequality for a complex perturbation of a d-dimensional massive Dirac operator $D_m, m\geq 0$ whose spectrum is $]-\infty , -m]\cup[m , +\infty[$. The difficulty of the study is that the unperturbed operator…

New estimates for eigenvalues of non-self-adjoint multi-dimensional Schr\"{o}dinger operators are obtained in terms of $L_{p}$-norms of the potentials. The results extend and improve those obtained previously. In particular, diverse…

This paper is mainly devoted to study time decay estimates of the higher-order Schr\"{o}dinger type operator $H=(-\Delta)^{m}+V(x)$ in $\mathbf{R}^{n}$ for $n>2m$ and $m\in\mathbf{N}$. For certain decay potentials $V(x)$, we first derive…

In this paper, we consider discrete Schr\"odinger operators of the form, \begin{equation*} (Hu)(n)= u({n+1})+u({n-1})+V(n)u(n). \end{equation*} We view $H$ as a perturbation of the free operator $H_0$, where $(H_0u)(n)= u({n+1})+u({n-1})$.…

Lieb-Thirring type estimates are proved for the sum of powers of negative eigenvalues of a Schr\"odinger type operator $(-\Delta)^l -V\mu$ where $\mu$ is a singular measure in $\mathbb{R}^d,$ satisfying a condition on the measure of balls…

We obtain accurate eigenvalues of the one-dimensional Schr\"odinger equation with a Hamiltonian of the form $H_{g}=H+g\delta (x)$, where $\delta (x)$ is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method…

This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…

Two-sided estimates for higher order eigenvalues are presented for a class of non-local Schr\"odinger operators by using the jump rate and the growth of the potential. For instance, let $L$ be the generator of a L\'evy process with L\'evy…

We consider the non-selfadjoint, semiclassical Schr\"odinger operator $\mathscr{L}(h) := -h^2\partial_x^2+e^{i\alpha}V$, where $\alpha \in (-\pi,\pi)$ and $V: \mathbb{R}\to \mathbb{R}_+$ is even and vanishes at exactly two (symmetric)…

This paper deals with the $L_p$-spectrum of Schr\"odinger operators on the hyperbolic plane. We establish Lieb-Thirring type inequalities for discrete eigenvalues and study their dependence on $p$. Some bounds on individual eigenvalues are…

We study a complex perturbation of a self-adjoint infinite band Schrodinger operator (defined in the form sense), and obtain the Lieb--Thirring type inequalities for the rate of convergence of the discrete spectrum of the perturbed operator…

Let L be a Schr\"odinger operator of the form L=-\Delta+V, where the nonnegative potential V satisfies a reverse H\"older inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted H\"older…

We prove a dispersive estimate for the evolution of Schroedinger operators H = -\Delta + V(x) in three dimensions. The potential should belong to the closure of bounded compactly-supported functions with respect to the golbal Kato norm.…

We propose a rigorous method for computing two-sided eigenvalue bounds of the Schr\"odinger operator $H=-\Delta+V$ with a confining potential on $\mathbb{R}^2$. The method combines domain truncation to a finite disk $D(R)$ on which the…

In this paper we examine the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a rapidly oscillating potential that is complex analytic in some neighborhood of the real line. Some of our results are…