Bounds on eigenfunctions of semiclassical operators with double characteristics

TL;DR

This paper establishes precise uniform bounds on low-lying eigenfunctions of certain semiclassical pseudodifferential operators with double characteristics, assuming ellipticity of quadratic approximations along these characteristics.

Contribution

It provides new sharp bounds for eigenfunctions of operators with double characteristics and complex symbols under ellipticity assumptions, advancing understanding in semiclassical analysis.

Findings

Sharp uniform bounds on eigenfunctions established

Results apply to operators with complex symbols and double characteristics

Ellipticity of quadratic approximations is crucial for bounds

Abstract

We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along the double characteristics are elliptic.