On the Limiting Absorption Principle at zero energy for a new class of possibly non self-adjoint Schr{\"o}dinger operators

TL;DR

This paper extends Mourre theory to non self-adjoint Schrödinger operators with complex potentials, demonstrating that certain conjugate operators can relax previous derivative conditions on the potential.

Contribution

It adapts Mourre theory to non self-adjoint operators and introduces new conjugate operators that weaken potential regularity requirements.

Findings

Relaxed conditions on potential derivatives for non self-adjoint Schrödinger operators.

Established limiting absorption principle at zero energy for a new class of operators.

Demonstrated effectiveness of different conjugate operators in spectral analysis.

Abstract

We recall a Moure theory adapted to non self-adjoint operators and we apply this theory to Schr{\"o}dinger operators with non real potentials, using different type of conjugate operators. We show that some conjugate operators permits to relax conditions on the derivatives of the potential that were required up to now.