Berezin-Toeplitz quantization and its kernel expansion

TL;DR

This paper surveys recent advances in Berezin-Toeplitz quantization, focusing on the asymptotic expansion of Toeplitz operators and their kernels, especially the calculation of initial coefficients.

Contribution

It provides a comprehensive overview of the latest results on the asymptotic behavior and coefficient calculation in Berezin-Toeplitz quantization.

Findings

Asymptotic expansion of Toeplitz operators analyzed

Calculation methods for first coefficients developed

Survey of recent progress in the field

Abstract

We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.