On the Localization of the Bergman Kernel and applications to Toeplitz theory

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Bibliographic Details
Main Author:	Finski, Siarhei
Format:	Preprint
Published:	2025
Subjects:	Complex Variables Algebraic Geometry Classical Analysis and ODEs Functional Analysis 32A25, 32U15, 42C05, 47B35, 15B05, 30C10
Online Access:	Acceder al recurso
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author	Finski, Siarhei
author_facet	Finski, Siarhei
contents	For a compact complex manifold endowed with a big line bundle and a Radon measure, we study the localization phenomena of the associated Bergman (or Christoffel-Darboux) kernel. For Bernstein-Markov measures, this results in the determination of the limiting off-diagonal Bergman measure, thereby confirming a conjecture of Zelditch. We then turn to applications in the theory of Toeplitz operators, showing in particular that they form an algebra under composition. Building on this, we then show that for Bernstein-Markov measures, the spectrum of Toeplitz operators equidistributes.
format	Preprint
id	arxiv_https___arxiv_org_abs_2508_03416
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	On the Localization of the Bergman Kernel and applications to Toeplitz theory Finski, Siarhei Complex Variables Algebraic Geometry Classical Analysis and ODEs Functional Analysis 32A25, 32U15, 42C05, 47B35, 15B05, 30C10 For a compact complex manifold endowed with a big line bundle and a Radon measure, we study the localization phenomena of the associated Bergman (or Christoffel-Darboux) kernel. For Bernstein-Markov measures, this results in the determination of the limiting off-diagonal Bergman measure, thereby confirming a conjecture of Zelditch. We then turn to applications in the theory of Toeplitz operators, showing in particular that they form an algebra under composition. Building on this, we then show that for Bernstein-Markov measures, the spectrum of Toeplitz operators equidistributes.
title	On the Localization of the Bergman Kernel and applications to Toeplitz theory
topic	Complex Variables Algebraic Geometry Classical Analysis and ODEs Functional Analysis 32A25, 32U15, 42C05, 47B35, 15B05, 30C10
url	https://arxiv.org/abs/2508.03416

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