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


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.


Ground State Energy Elliptic Operator Harnack Inequality Lebesgue Dominate Convergence Theorem Martin Boundary 
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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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