Abstract
In this paper, we extend the result of Donig[Do] and show the finiteness of the lower spectrum of the uniformly elliptic operators−▿·(A(x)▿)+q with singular potentialsq which belong to the Kato class. Even in the case of the Schrödinger operator−Δ+q, our proof simplifies the one in [Do].
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References
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[Si] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc., 7(1982), 447–526.
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Kurata, K. A remark on finiteness of the lower spectrum of uniformly elliptic operators with singular potentials. Integr equ oper theory 36, 212–219 (2000). https://doi.org/10.1007/BF01202096
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DOI: https://doi.org/10.1007/BF01202096