Related papers: Asymptotics of resonances for a schrodinger operat…
We consider complex resonances for discrete and continuous Schr\"odinger operators, and we show that the resonances of discrete models converge to resonances of continuous models in the continuum limit. The potential is supposed to be a sum…
We prove sharp upper bounds for the number of resonances in boxes of size 1 at high frequency for the Laplacian on finite volume surfaces with hyperbolic cusps. As a corollary, we obtain a Weyl asymptotic for the number of resonances in…
In this paper, we first deduce the asymptotic expansions of resolvent of $H=(-\Delta)^2+V$ with the presence of resonance or eigenvalue at the degenerate zero threshold for $d\geq5$. In particular, we identify these resonance spaces for…
We present some results on the monotonicity of some traces involving functions of self-adjoint operators with respect to the natural ordering of their associated quadratic forms. We also apply these results to complete a proof of the Wegner…
We introduce and study the following model for random resonances: we take a collection of point interactions $\Upsilon_j$ generated by a simple finite point process in the 3-D space and consider the resonances of associated random…
Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding and an integral operator of Volterra type. These lead to asymptotic formulae for the approximation numbers and certain other s-numbers.
We fnd the asymptotics of eigenvalues of polynomially compact zero order pseudodiferential operators, the motivating example being the Neumann- Poincare operator in linear elasticity.
We study upper bounds and the asymptotic behavior of high order moments for solutions to a family of linear and nonlinear Schroedinger equations.
We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
We prove asymptotics of the Christoffel function, $\lambda_L(\xi)$, of a continuum Schr\"odinger operator for points in the interior of the essential spectrum under some mild conditions on the spectral measure. It is shown that…
We prove that the results in scattering theory that involve resonances are still valid for non-analytic potentials, even if the notion of resonance is not defined in this setting. More precisely, we show that if the potential of a…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
We consider a $2\times 2$ system of 1D semiclassical differential operators with two Schr\"odinger operators in the diagonal part and small interactions of order $h^\nu$ in the off-diagonal part, where $h$ is a semiclassical parameter and…
We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\mathbb{R}^{2d}$, $d\geq 1$. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give…
We consider a general elliptic operator in an infinite multi-dimensional cylinder with several distant perturbations; this operator is obtained by ``gluing'' several single perturbation operators $\mathcal{H}^{(k)}$, $k=1,\ldots,n$, at…
We consider 2-dimensional Schroedinger operator with the non-degenerating magnetic field in the domain with the boundary and under certain non-degeneracy assumptions we derive spectral asymptotics with the remainder estimate better than…
In this paper, we introduce a new family of functions to construct Schr\"odinger operators with embedded eigenvalues. This particularly allows us to construct discrete Schr\"odinger operators with arbitrary prescribed sets of eigenvalues.
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…
The purpose of this paper is to describe asymptotic formulas for determinants of certain operators that are analogues of Wiener-Hopf operators. The determinant formulas yield information about the distribution functions for certain random…