The explicit forms and zeros of the Bergman kernel function for Hartogs type domains

DOI10.1016/j.jfa.2012.01.021zbMath1251.32002OpenAlexW2050421956MaRDI QIDQ413200

Jong-Do Park, HeungJu Ahn

Publication date: 4 May 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2012.01.021

zbMATH Keywords

Bergman kernel functionbounded symmetric domainStirling numberRouth-Hurwitz theoremHartogs domainvirtual Bergman kernel

Mathematics Subject Classification ID

Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items

Zero problems of the Bergman kernel function on the first type of Cartan-Hartogs domain ⋮ Unnamed Item ⋮ The zeros of the Bergman kernel for some Reinhardt domains ⋮ An application of a Diederich-Ohsawa theorem in characterizing some Hartogs domains ⋮ On holomorphic isometric immersions of nonhomogeneous Kähler-Einstein manifolds into the infinite dimensional complex projective space ⋮ Automorphisms of normal quasi-circular domains ⋮ Unnamed Item ⋮ The explicit forms and zeros of the Bergman kernel for 3-dimensional Hartogs triangles ⋮ On the zeros of the slice Bergman kernels for the upper half space and the unit ball on quaternions and Clifford algebras ⋮ Uniform extendibility of the Bergman kernel for generalized minimal balls ⋮ Bergman kernel function for Hartogs domains over bounded homogeneous domains ⋮ Properties of squeezing functions and global transformations of bounded domains ⋮ The Bergman kernel function for intersections of some cylindrical domains and Lauricella's hypergeometric function ⋮ Boundary behavior of the Bergman kernel for generalized Fock-Bargmann-Hartogs domains ⋮ The Bergman kernels of generalized Bergman-Hartogs domains ⋮ Balanced metrics on some Hartogs type domains over bounded symmetric domains

Cites Work

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• The Bergman kernel of the symmetrized polydisc in higher dimensions has zeros
• Lu Qi-Keng conjecture and Hua domain
• Zeros of Bergman kernels on some Hartogs domains
• A compact Kähler surface of negative curvature not covered by the ball
• The Lu Qi-Keng conjecture fails for strongly convex algebraic domains
• An explicit computation of the Bergman kernel function
• The Bergman kernel of the minimal ball and applications
• The Bergman kernels on Cartan-Hartogs domains
• A Forelli-Rudin construction and asymptotics of weighted Bergman kernels
• Geometry of the symmetrized polydisc
• Analysis and geometry on complex homogeneous domains
• New classes of domains with explicit Bergman kernel
• Lu Qi-Keng's problem on some complex ellipsoids
• Weighted Bergman kernels and virtual Bergman kernels
• The Bergman kernel of complex ovals and multivariable hypergeometric functions
• Function spaces and reproducing kernels on bounded symmetric domains
• New formulas of the Bergman kernels for complex ellipsoids in $\mathbb {C}^2$
• On the Lu Qi-Keng Conjecture
• On the Forelli-Rudin construction and weighted Bergman projections
• 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
• The Lu Qi-Keng conjecture fails generically
• On the theory of functions of several complex variables. II. A complex orthonormal system in the hyperbolic space of the Lie-hypersphere
• A note on the Bergman kernel

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