Resolvent estimates for non-selfadjoint operators with double characteristics

TL;DR

This paper establishes polynomial bounds on the resolvent of certain non-selfadjoint semiclassical operators with double characteristics, under ellipticity assumptions on the quadratic approximation, advancing understanding of their spectral behavior.

Contribution

It provides new resolvent estimates for non-selfadjoint operators with double characteristics, assuming ellipticity of the quadratic approximation, which was not previously established.

Findings

Polynomial resolvent bounds inside the pseudospectrum

Resolvent estimates depend on ellipticity of quadratic approximation

Advances spectral analysis of non-selfadjoint operators with double characteristics

Abstract

We study resolvent estimates for non-selfadjoint semiclassical pseudodifferential operators with double characteristics. Assuming that the quadratic approximation along the double characteristics is elliptic, we obtain polynomial upper bounds on the resolvent in a suitable region inside the pseudospectrum.