Annales Henri Poincaré

, Volume 8, Issue 7, pp 1371–1399 | Cite as

Distant Perturbations of the Laplacian in a Multi-Dimensional Space

  • Denis I. Borisov


We consider the Laplacian in \({\mathbb{R}}^{n}\) perturbed by a finite number of distant perturbations that 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 a convergence theorem and the asymptotic expansions for the eigenelements. Some examples of the possible distant perturbations are given; they may be a multiplication operator, second order differential operator, magnetic Schrödinger operator, integral operator, and δ-potential.


Asymptotic Expansion Dirac Operator Nontrivial Solution Asymptotic Formula Discrete Spectrum 
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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Nuclear Physics InstituteAcademy of SciencesŘež near PragueCzechia
  2. 2.Bashkir State Pedagogical UniversityUfaRussia

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