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arXiv · 1912.05447

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

Martin Karuhanga·Eugene Shargorodsky
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Abstract

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

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Martin Karuhanga, Eugene Shargorodsky. 2019-12-10. On negative eigenvalues of two-dimensional Schroedinger operators with singular potentials. https://doi.org/10.1063/5.0004481

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