The adjoint of a composition operator via its action on the Szegő kernel

DOI10.1007/s13324-018-0215-yzbMath1395.30013OpenAlexW2791231456MaRDI QIDQ1668697

Steven R. Bell

Publication date: 29 August 2018

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13324-018-0215-y

zbMATH Keywords

Bergman kernelquadrature domainsdouble quadrature domains

Mathematics Subject Classification ID

Kernel functions in one complex variable and applications (30C40) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items

The Cauchy integral formula, quadrature domains, and Riemann mapping theorems

Cites Work

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• Szegő coordinates, quadrature domains, and double quadrature domains
• Unique continuation theorems for the \(\bar \partial\)-operator and applications
• A new class of operators and a description of adjoints of composition operators
• Adjoints of rationally induced composition operators
• Boundary behavior of proper holomorphic correspondences
• Application of half-order differentials on Riemann surfaces to quadrature identities for arc-length
• An extension of the Nevanlinna theory
• Domains on which analytic functions satisfy quadrature identities
• A Beurling-type theorem
• Non-vanishing of the Bergman kernel function at boundary points of certain domains in \(\mathbb{C}^n\)
• Topics on holomorphic correspondences
• Quadrature identities and the Schottky double
• Adjoints of composition operators with rational symbol
• The Cauchy Transform, Potential Theory and Conformal Mapping
• Complexity of the classical kernel functions of potential theory
• Ideals in Rings of Analytic Functions with Smooth Boundary Values

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