On the coefficients of the asymptotic expansion of the kernel of Berezin-Toeplitz quantization

TL;DR

This paper introduces new methods, based on stationary phase formulas, for computing the coefficients in the asymptotic expansion of Berezin-Toeplitz quantization kernels and their compositions.

Contribution

It provides novel computational techniques for asymptotic expansion coefficients in Berezin-Toeplitz quantization using Melin-Sjöstrand's stationary phase formula.

Findings

New methods for coefficient computation in asymptotic expansions

Application of stationary phase formula to Berezin-Toeplitz kernels

Enhanced understanding of kernel composition in quantization

Abstract

We give new methods for computing the coefficients of the asymptotic expansions of the kernel of Berezin-Toeplitz quantization obtained recently by Ma-Marinescu, and of the composition of two Berezin-Toeplitz quantizations. Our main tool is the stationary phase formula of Melin-Sj\"{o}strand.