Negative eigenvalues of non-local Schrödinger operators with sign-changing potentials
Author:
Abstract
Simon’s results on the negative spectrum of recurrent Schrödinger operators ( d = 1 , 2 d=1,2 ) are extended to a wider class of potentials and to non-local operators. An example of L 1 − 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 ≥ 3 d\geq 3 ) showing that the assumptions on the potential for the validity of the Cwikel-Lieb-Rozenblum estimate can’t be improved significantly.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
https://www.ams.org/proc/2023-151-11/S0002-9939-2023-16489-8/S0002-9939-2023-16489-8.pdf
Reference11 articles.
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3. Bounds on the eigenvalues of the Laplace and Schroedinger operators;Lieb, Elliott;Bull. Amer. Math. Soc.,1976
4. On general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities;Molchanov, Stanislav,2010
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