Bernstein-Markov measures and Toeplitz theory
Complex Variables
2025-06-03 v1 Algebraic Geometry
Functional Analysis
Spectral Theory
Abstract
We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an application, we derive a Szeg\H{o}-type spectral equidistribution result for this class of operators. A key component of our approach is the off-diagonal asymptotic analysis of the Bergman kernel, also known as the Christoffel-Darboux kernel.
Cite
@article{arxiv.2506.01610,
title = {Bernstein-Markov measures and Toeplitz theory},
author = {Siarhei Finski},
journal= {arXiv preprint arXiv:2506.01610},
year = {2025}
}