Work

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

Year: 2020

Type: article

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.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0004481

Authors: Martin Karuhanga, Eugene Shargorodsky

Institutions: Mbarara University of Science and Technology, King's College London

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Commonwealth Scholarship Commission

Award: G5132385248