An exotic calculus of Berezin-Toeplitz operators

Abstract

This paper generalizes composition formulae of Berezin-Toeplitz operators for quantizations of smooth functions on a compact K\"ahler manifold to certain exotic symbol classes. This is accomplished via careful analysis of the kernel of these operators using Melin and Sj\"ostrand's method of complex stationary phase. This provides a functional calculus result, a trace formula, and a parametrix construction for a larger symbol class. These results are used in proving a probabilistic Weyl-law for randomly perturbed Toeplitz operators.Comment: 37 page