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

## TL;DR

This paper develops a multiplier method to establish conditions for the absence of eigenvalues in non-self-adjoint Robin Laplacians on the half-space, also deriving resolvent estimates and extending results even to the self-adjoint case.

## Contribution

It introduces a new multiplier technique to analyze eigenvalue absence and resolvent bounds for Robin Laplacians with variable complex boundary conditions.

## Key findings

- Eigenvalues are absent under certain boundary conditions.
- Uniform resolvent estimates are established.
- Some results are novel even for self-adjoint operators.

## 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.