On negative eigenvalues of two-dimensional Schrödinger operators with singular potentials

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Abstract

We present upper estimates for the number of negative eigenvalues of two-dimensional Schrödinger operators with potentials generated by Ahlfors regular measures of arbitrary fractional dimension α ∈ (0, 2]. The estimates are given in terms of integrals of the potential with a logarithmic weight and of its L log L type Orlicz norms. In the case α = 1, our results are stronger than the known ones about Schrödinger operators with potentials supported by Lipschitz curves.

Original languageEnglish
Article number0004481
Number of pages43
JournalJOURNAL OF MATHEMATICAL PHYSICS
Volume61
Issue number5
DOIs
Publication statusPublished - 20 May 2020

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