Abstract
Let V: R N→[0, ∞] be a measurable function, and λ>0 be a parameter. We consider the behaviour of the spectral bound of the operator 1/2Δ−λV as a function of λ. In particular, we give a formula for the limiting value as λ→∞, in terms of the integrals of V over subsets of R N on which the Laplacian with Dirichlet boundary conditions has prescribed values. We also consider the question whether this limiting value is attained for finite λ.
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Arendt, W., Batty, C.J.K. The spectral bound of Schrödinger operators. Potential Anal 5, 207–230 (1996). https://doi.org/10.1007/BF00282361
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DOI: https://doi.org/10.1007/BF00282361