# Semiclassical asymptotics for nonselfadjoint harmonic oscillators

## TL;DR

This paper investigates the spectral properties of nonselfadjoint perturbations of semiclassical harmonic oscillators, providing bounds on the resolvent under certain dynamical conditions even without geometric control.

## Contribution

It offers new spectral estimates for nonselfadjoint harmonic oscillators under dynamical assumptions, extending understanding beyond geometric control conditions.

## Key findings

- Established upper bounds on the resolvent near the real axis.
- Derived spectral estimates under specific dynamical assumptions.
- Extended spectral analysis to cases lacking geometric control.

## Abstract

We consider nonselfadjoint perturbations of semiclassical harmonic oscillators. Under appropriate dynamical assumptions, we establish some spectral estimates such as upper bounds on the resolvent near the real axis when no geometric control condition is satisfied.