Related papers: On Lieb-Thirring inequalities for multidimensional…

We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as…

We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…

We show that phase space bounds on the eigenvalues of Schr\"{o}dinger operators can be derived from universal bounds recently obtained by E. M. Harrell and the author via a monotonicity property with respect to coupling constants. In…

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.

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of…

Given a potential $V$ and the associated Schr\"odinger operator $-\Delta+V$, we consider the problem of providing sharp upper and lower bound on the energy of the operator. It is known that if for example $V$ or $V^{-1}$ enjoys suitable…

Let $H := H_{0} + V$ and $H_{\perp} := H_{0,\perp} + V$ be respectively perturbations of the free Schr\"odinger operators $H_{0}$ on $L^{2}\big(\mathbb{R}^{2d+1}\big)$ and $H_{0,\perp}$ on $L^{2}\big(\mathbb{R}^{2d}\big)$, $d \geq 1$ with…

We introduce multidimensional Schur multipliers and characterise them generalising well known results by Grothendieck and Peller. We define a multidimensional version of the two dimensional operator multipliers studied recently by Kissin…

We show that for a Schr\"odinger operator with bounded potential on a manifold with cylindrical ends the space of solutions which grows at most exponentially at infinity is finite dimensional and, for a dense set of potentials (or,…

We consider Schr\"odinger operators with complex-valued decreasing potentials on the half-line. Such operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the…

It is shown that the 1-dimensional lattice Schrodinger operator with potential given by a non-zero multiple of the Moebius function has positive Lyapounov exponent. In view of the classical theory of random Schrodinger operators, this may…

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…

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators…

We consider Schr\"odinger operators with complex decaying potentials on the lattice. Using some classical results from Complex Analysis we obtain some trace formulae and using them estimate globally all zeros of the Fredholm determinant in…

The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…

We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for…

This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…

We consider Schroedinger operators on regular metric trees and prove Lieb-Thirring and Cwikel-Lieb-Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show…

The research on spectral inequalities for discrete Schrodinger Operators has proved fruitful in the last decade. Indeed, several authors analysed the operator's canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we…

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for…