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Journal d’Analyse Mathématique

, Volume 66, Issue 1, pp 57–83 | Cite as

On the localization of binding for Schrödinger operators and its extension to elliptic operators

  • Yehuda Pinchover
Article

Abstract

In this paper we study the asymptotic behavior of the ground state energyE(R) of the Schrödinger operatorP R=−Δ+V 1(x)+V 2(x-R),x,R ∈ℝn, where the potentialsV i are small perturbations of the Laplacian in ℝn,n≥3. The methods presented here apply also in the investigation of the ground state energyE(g) of the operatorPg=P+V 1(x)+V 2(gx), x ∈X,gG, whereP g is an elliptic operator which is defined on a noncompact manifoldX, G is a discrete group acting onX by diffeomorphismsG×X∈(g, x)→gxX, andP is aG-invariant elliptic operator which is subcritical inX.

Keywords

Ground State Energy Elliptic Operator Harnack Inequality Lebesgue Dominate Convergence Theorem Martin Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Magnes Press, The Hebrew University 1995

Authors and Affiliations

  • Yehuda Pinchover
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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