Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space
Spectral Theory
2020-08-28 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
By developing the method of multipliers, we establish sufficient conditions which guarantee the total absence of eigenvalues of the Laplacian in the half-space, subject to variable complex Robin boundary conditions. As a further application of this technique, uniform resolvent estimates are derived under the same assumptions on the potential. Some of the results are new even in the self-adjoint setting, where we obtain quantum-mechanically natural conditions.
Keywords
Cite
@article{arxiv.1812.05348,
title = {Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space},
author = {Lucrezia Cossetti and David Krejcirik},
journal= {arXiv preprint arXiv:1812.05348},
year = {2020}
}
Comments
Minor corrections, references added, accepted for publication in the Proceedings of the London Mathematical Society