Toeplitz operators on symplectic manifolds

TL;DR

This paper investigates Toeplitz operators on symplectic manifolds using Berezin-Toeplitz quantization, providing asymptotic expansions, characterizations, and semi-classical limit properties for non-compact cases.

Contribution

It offers a detailed asymptotic expansion of the Bergman kernel and characterizes Toeplitz operators in this context, extending understanding to non-compact manifolds and orbifolds.

Findings

Asymptotic expansion of the Bergman kernel obtained

Characterization of Toeplitz operators via asymptotics

Semi-classical limits established for non-compact manifolds

Abstract

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.