Just analysis: the Poisson-Szegő-Bergman kernel

DOI10.1007/s12220-022-01075-yzbMath1504.30009OpenAlexW4307648413MaRDI QIDQ2091074

Steven R. Bell

Publication date: 31 October 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-022-01075-y

zbMATH Keywords

Bergman kernelPoisson kernelSzegő kernel

Mathematics Subject Classification ID

Capacity and harmonic measure in the complex plane (30C85) Kernel functions in one complex variable and applications (30C40)

Cites Work

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• Szegő coordinates, quadrature domains, and double quadrature domains
• The Szegő kernel and proper holomorphic mappings to a half plane
• The Dirichlet and Neumann and Dirichlet-to-Neumann problems in quadrature, double quadrature, and non-quadrature domains
• On the classical Dirichlet problem in the plane with rational data
• Ahlfors maps, the double of a domain, and complexity in potential theory and conformal mapping
• Complexity in complex analysis.
• Ruminations on Hejhal's theorem about the Bergman and Szegő kernels
• Real algebraic geometry of real algebraic Jordan curves in the plane and the Bergman kernel
• Various types of orthogonalization
• The Cauchy Transform, Potential Theory and Conformal Mapping
• Singularities encountered by the analytic continuation of solutions to dirichlet's problem
• Complexity of the classical kernel functions of potential theory

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