Analytic Berezin-Toeplitz operators

TL;DR

This paper develops new analytic microlocal analysis tools on Kähler manifolds and demonstrates that Berezin-Toeplitz operators with analytic symbols form an algebra, also providing a simplified proof of Bergman kernel asymptotics.

Contribution

It introduces novel tools for analytic microlocal analysis and proves the algebra property of Berezin-Toeplitz operators with analytic symbols.

Findings

Berezin-Toeplitz operators with analytic symbols form an algebra

Provided a short proof of Bergman kernel asymptotics with exponentially small error

Developed new analytic microlocal analysis tools for Kähler manifolds

Abstract

We introduce new tools for analytic microlocal analysis on K\"ahler manifolds. As an application, we prove that the space of Berezin-Toeplitz operators with analytic contravariant symbol is an algebra. We also give a short proof of the Bergman kernel asymptotics up to an exponentially small error.