Subelliptic Resolvent Estimates for Non-self-adjoint Semiclassical Schrodinger Operators

TL;DR

This paper establishes subelliptic resolvent estimates for a class of semiclassical non-self-adjoint Schrödinger operators with purely imaginary potentials, focusing on spectral parameters near the imaginary axis.

Contribution

It provides the first subelliptic resolvent estimates for non-self-adjoint Schrödinger operators with purely imaginary potentials in a semiclassical setting.

Findings

Resolvent estimates hold in a parabolic neighborhood of the imaginary axis.

The results extend understanding of spectral behavior for non-self-adjoint operators.

New techniques for handling purely imaginary potentials in semiclassical analysis.

Abstract

In this paper we prove a subelliptic resolvent estimate for a class of semiclassical non-self-adjoint Schr\"odinger operators with purely imaginary potentials when the spectral parameter is in a parabolic neighborhood of the imaginary axis.