Berezin-Toeplitz quantization on Kaehler manifolds

TL;DR

This paper investigates Berezin-Toeplitz quantization on Kähler manifolds, deriving asymptotic expansions and explicit kernel computations, with applications to estimating the norm of Donaldson's Q-operator.

Contribution

It provides explicit calculations of asymptotic expansions and kernels for Berezin-Toeplitz operators on Kähler manifolds, advancing understanding of their properties.

Findings

Computed first terms of the Berezin-Toeplitz kernel expansion

Derived explicit formulas for the composition of Berezin-Toeplitz operators

Estimated the norm of Donaldson's Q-operator

Abstract

We study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the Berezin-Toeplitz operators, and of the composition of two Berezin-Toeplitz operators. As application we estimate the norm of Donaldson's Q-operator.