On the localization of binding for Schrödinger operators and its extension to elliptic operators
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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,g ∈G, 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)→gx∈X, andP is aG-invariant elliptic operator which is subcritical inX.
KeywordsGround State Energy Elliptic Operator Harnack Inequality Lebesgue Dominate Convergence Theorem Martin Boundary
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