Distant perturbations of the Laplacian in a multi-dimensional space

Abstract

We consider the Laplacian in $\mathbb{R}^n$ perturbed by a finite number of distant perturbations those are abstract localized operators. We study the asymptotic behaviour of the discrete spectrum as the distances between perturbations tend to infinity. The main results are the convergence theorem and the asymptotics expansions for the eigenelements. Some examples of the possible distant perturbations are given; they are potential, second order differential operator, magnetic Schrodinger operator, integral operator, and $\d$-potential.