Finiteness of the lower spectrum of Schrödinger operators with singular potentials
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- by Jörg Donig PDF
- Proc. Amer. Math. Soc. 112 (1991), 489-501 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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