Bernstein-Markov measures and Toeplitz theory

2025/06/02 by Finski, Siarhei
#15B05 #32A25 #32U15 #42C05 #47B35 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2506.01610

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 Szegő-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.

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Related

• Toeplitz operators, submultiplicative filtrations and weighted Bergman kernels
• Toeplitz operators with analytic symbols
• Bergman kernel estimates and Toeplitz operators on holomorphic line bundles
• Semi-Classical Asymptotic Expansions for Toeplitz Quantizations on Complex Manifolds and Orbifolds
• On the Localization of the Christoffel-Darboux Kernel