Resolvent Estimates for Non-Self-Adjoint Magnetic Schr\"{o}dinger Operators

TL;DR

This paper establishes resolvent estimates for semiclassical magnetic Schrödinger operators with complex potentials, providing bounds near the imaginary axis under specific conditions on the potentials.

Contribution

It introduces new resolvent estimates for non-self-adjoint magnetic Schrödinger operators with complex electric potentials, expanding understanding of their spectral behavior.

Findings

Resolved spectral parameter bounds in a parabolic neighborhood of the imaginary axis.

Derived resolvent estimates under conditions on magnetic and electric potentials.

Enhanced spectral analysis for non-self-adjoint magnetic Schrödinger operators.

Abstract

We examine semiclassical magnetic Schr\"{o}dinger operators with complex electric potentials. Under suitable conditions on the magnetic and electric potentials, we prove a resolvent estimate for spectral parameters in an unbounded parabolic neighborhood of the imaginary axis.