Work

An exotic calculus of Berezin–Toeplitz operators

Year: 2025

Type: article

Abstract: We develop a calculus of Berezin–Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and the power of the line bundle. The properties of this quantization are obtained via careful analysis of the kernels of the operators using Melin and Sjöstrand's method of complex stationary phase. We obtain a functional calculus result, a trace formula, and a parametrix construction for this larger class of functions. These results are crucially used in proving a probabilistic Weyl‐law for randomly perturbed (standard) Berezin–Toeplitz operators in Oltman (arXiv:2207.09599).

Source: Mathematika

DOI: 10.1112/mtk.70016

Author: Izak Oltman

Institution: Northwestern University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: National Science Foundation