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

DOI10.1007/S40315-018-0246-2zbMath1404.30007OpenAlexW2807319511WikidataQ129731773 ScholiaQ129731773MaRDI QIDQ1634276

Steven R. Bell

Publication date: 18 December 2018

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-018-0246-2

zbMATH Keywords

Bergman kernelSzego kerneldouble quadrature domains

Mathematics Subject Classification ID

Conformal mappings of special domains (30C20) Kernel functions in one complex variable and applications (30C40) Connections of harmonic functions with differential equations in two dimensions (31A35)

Cites Work

• Szegő coordinates, quadrature domains, and double quadrature domains
• Unique continuation theorems for the \(\bar \partial\)-operator and applications
• Application of half-order differentials on Riemann surfaces to quadrature identities for arc-length
• Domains on which analytic functions satisfy quadrature identities
• The adjoint of a composition operator via its action on the Szegő kernel
• Quadrature domains and their applications. The Harold S. Shapiro anniversary volume. Expanded version of talks and papers presented at a conference on the occasion of the 75th birthday of Harold S. Shapiro, Santa Barbara, CA, USA, March 2003
• Quadrature identities and the Schottky double
• The Cauchy Transform, Potential Theory and Conformal Mapping
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