Berezin transform in polynomial Bergman spaces

2008/07/02 by Yacin Ameur, Håakan Hedenmalm, Ameur, Yacin +3 · 3 citations
Mathematics · #30C10 #30C40 #31A05 #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0807.0369

openalex publication_date 2008/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the reproducing kernel for weighted polynomial Bergman spaces and consider applications to the Berezin transform. Some of our results have applications in random matrix theory, a topic which we discuss in a separate (companion) paper.

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• Fisher-Hartwig asymptotics for non-Hermitian random matrices
• Universality for fluctuations of counting statistics of random normal matrices
• Smallest gaps of the two-dimensional Coulomb gas

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