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Eigenvalues of Schrödinger operators with potential asymptotically homogeneous of degree -2

Hassell, Andrew; Marshall, Simon


We strengthen and generalise a result of Kirsch and Simon on the behaviour of the function NL(E), the number of bound states of the operator L = Δ+V in ℝd below -E. Here V is a bounded potential behaving asymptotically like P(ω)r-2 where P is a function on the sphere. It is well known that the eigenvalues of such an operator are all nonpositive, and accumulate only at 0. If the operator ΔSd-1 +P on the sphere Sd-1 has negative eigenvalues -μ1, ⋯ ,-μn less than -(d-2)2/4, we prove that NL(E) may...[Show more]

CollectionsANU Research Publications
Date published: 2008-03-13
Type: Journal article
Source: Transactions of the American Mathematical Society
DOI: 10.1090/S0002-9947-08-04479-6


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