New formulas of the Bergman kernels for complex ellipsoids in $\mathbb {C}^2$

DOI10.1090/S0002-9939-08-09576-2zbMath1157.32006MaRDI QIDQ3542039

Jong-Do Park

Publication date: 27 November 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

hypergeometric functionsBergman kernelBergman spacescomplex ellipsoidsSzegő kernel

Mathematics Subject Classification ID

Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Other basic hypergeometric functions and integrals in several variables (33D70)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Proper holomorphic mappings and the Bergman projection
• An explicit computation of the Bergman kernel function
• Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\)
• On the Bergman invariant and curvatures of the Bergman metric
• The Bergman kernel of complex ovals and multivariable hypergeometric functions
• The Bergman Kernel Function and Propert Holomorphic Mappings
• The Bergman kernel function: Explicit formulas and zeroes
• Proper holomorphic liftings and new formulas for the Bergman and Szegő kernels
• Bergman kernel for the two-dimensional balls
• The Bergman kernel function of some Reinhardt domains
• A note on the Bergman kernel

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