Distant perturbations of the Laplacian in a multi-dimensional space

Details Distant perturbations of the Laplacian in a multi-dimensional space Distant perturbations of the Laplacian in a multi-dimensional space

2006-08-02

arxiv.org/abs/math-ph/0608006v2

Physics

Mathematical Physics

Scientific paper

10.1007/s00023-007-0338-4

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.

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