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Finiteness of the lower spectrum of Schrödinger operators with singular potentials


Author: Jörg Donig
Journal: Proc. Amer. Math. Soc. 112 (1991), 489-501
MSC: Primary 35P05; Secondary 35J10
DOI: https://doi.org/10.1090/S0002-9939-1991-1043408-0
MathSciNet review: 1043408
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Abstract: We assume that $ q:{\mathbb{R}^m} \to \mathbb{R}(m \geq 3)$ is a measurable function with the property that its negative and positive parts, respectively, belong to the Kato class $ K({\mathbb{R}^m})$ and $ {K_{loc}}({\mathbb{R}^m})$. We prove a conjecture by B. Simon concerning the finiteness of the lower spectrum of an s.a. realization of the Schrödinger expression $ - \Delta + q$ in $ {L^2}({\mathbb{R}^m})$ bounded from below.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1043408-0
Article copyright: © Copyright 1991 American Mathematical Society

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