Lieb-Thirring and Jensen sums for non-self-adjoint Schr\"odinger operators on the half-line
Spectral Theory
2022-03-01 v3 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We prove upper and lower bounds for sums of eigenvalues of Lieb-Thirring type for non-self-adjoint Schr\"odinger operators on the half-line. The upper bounds are established for general classes of integrable potentials and are shown to be optimal in various senses by proving the lower bounds for specific potentials. We consider sums that correspond to both the critical and non-critical cases.
Keywords
Cite
@article{arxiv.2111.09629,
title = {Lieb-Thirring and Jensen sums for non-self-adjoint Schr\"odinger operators on the half-line},
author = {Leonid Golinskii and Alexei Stepanenko},
journal= {arXiv preprint arXiv:2111.09629},
year = {2022}
}
Comments
41 pages, 2 figures, Propositions 2.6 and 2.10 have been added