Eigenvalue bounds for Schrödinger operators with complex potentials

We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan, and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our ma...

Full description

Bibliographic Details
Main Author: Frank, Rupert L.
Format: Text
Language:unknown
Published: arXiv 2010
Subjects:
Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
Sogge
laptev
Online Access:https://dx.doi.org/10.48550/arxiv.1005.2785
https://arxiv.org/abs/1005.2785
Description
Summary:We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan, and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz, and Sogge. : 7 pages

Similar Items