Resolvent estimates for elliptic quadratic differential operators

TL;DR

This paper establishes precise bounds on the resolvent operator for a class of non-selfadjoint elliptic quadratic differential operators, enhancing understanding of their spectral properties in the semiclassical regime.

Contribution

It provides the first sharp resolvent estimates for non-selfadjoint elliptic quadratic operators within the interior of the symbol's range.

Findings

Sharp resolvent bounds are derived.

Results apply to semiclassical elliptic quadratic operators.

Improves spectral analysis understanding for non-selfadjoint operators.

Abstract

Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.