On the number of negative eigenvalues of Schrödinger operators with an Aharanov-Bohm magnetic field

Balinsky, Alexander ORCID: https://orcid.org/0000-0002-8151-4462, Evans, William Desmond and Lewis, R. T. 2001. On the number of negative eigenvalues of Schrödinger operators with an Aharanov-Bohm magnetic field. Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences 457 (2014) , pp. 2481-2489. 10.1098/rspa.2001.0851

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Abstract

It is proved that for V+=max(V,0) in the subspace L1(R+ ; L∞(S1); r dr) of L1(R2), there is a Cwikel–Lieb–Rosenblum–type inequality for the number of negative eigen2 R values of the operator ((1/i)∇ + A)2 — V in L2(R2) when A is an Aharonov-Bohm magnetic potential with non-integer flux. It is shown that the L1(R+, L∞ (S1),r dr)-norm cannot be replaced by the L1(R2)-norm in the inequality.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
ISSN:	1471-2946
Related URLs:	Publisher
Last Modified:	17 Oct 2022 08:59
URI:	https://orca.cardiff.ac.uk/id/eprint/1687

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