Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space

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.

arXiv commentMinor corrections, references added, accepted for publication in the Proceedings of the London Mathematical Society

References in corpus (6)

• An extension problem related to the fractional Laplacian
• Eigenvalue bounds for Schrödinger operators with complex potentials
• Eigenvalues of Robin Laplacians in infinite sectors
• Tunneling between corners for Robin Laplacians
• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• Virial identity and dispersive estimates for the $n$-dimensional Dirac equation

Cited by in corpus (4)

• Keller-type bounds for Dirac operators perturbed by rigid potentials
• Localization of eigenvalues for non-self-adjoint Dirac and Klein-Gordon operators
• The virial theorem and the method of multipliers in spectral theory
• From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation