Negative eigenvalues of non-local Schrödinger operators with sign-changing potentials

Molchanov, S.; Vainberg, B.

doi:10.1090/proc/16489

Negative eigenvalues of non-local Schrödinger operators with sign-changing potentials
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by S. Molchanov and B. Vainberg

Proc. Amer. Math. Soc. 151 (2023), 4757-4770

DOI: https://doi.org/10.1090/proc/16489

Published electronically: June 30, 2023

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Abstract:

Simon’s results on the negative spectrum of recurrent Schrödinger operators ($d=1,2$) are extended to a wider class of potentials and to non-local operators. An example of $L^1-$potental is constructed for which the essential spectrum of two dimensional Schrödinger operator covers the whole axis. Some counterexamples are provided for transient operators ($d\geq 3$) showing that the assumptions on the potential for the validity of the Cwikel-Lieb-Rozenblum estimate can’t be improved significantly.

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