• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.283-290
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• 1996

We can expect a close relationship between the Bergman kernel and the Szego kernel of a domain because we can change boundary integrals to solid integrals via Green's identity.

• East Asian mathematical journal
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• v.19 no.1
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• pp.49-61
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• 2003

We study the asymptotic boundary behavior of the Bergman kernel function on the diagonal, the Bergman metric and the holomorphic sectional curvatures of the Bergman metric in bounded strongly pseudoconvex domains.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.199-213
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• 2006

We compute the holomorphic derivative of the harmonic measure associated to a $C^\infty$bounded domain in the plane and show that the exact Bergman kernel function associated to a $C^\infty$ bounded domain in the plane relates the derivatives of the Ahlfors map and the Szego kernel in an explicit way. We find several formulas for the exact Bergman kernel and the Szego kernel and the harmonic measure. Finally we survey some other properties of the holomorphic derivative of the harmonic measure.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.69-83
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• 2012

In this note, we present certain circular domain, named Forelli-Rudin construction or Hua construction, which is built on Cartan domains. We compute the explicit Bergman kernel for it and get the corresponding weighted Bergman kernel on its base.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.183-191
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• 2005

In this paper we find the Laurent series expansions representing the reproducing kernels. Also we find the number of zeroes of the exact Bergman kernel via parallel slit domain in order to relate the exact Bergman kernel to an extremal problem.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.115-123
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• 1994

The Bergman kernel is closely connected to mapping problems in complex analysis. For example, the Riemann mapping function is witten down in terms of the Bergman kernel. Hence, information about the bergman kernel gives information about mappings. In this note, we prove the following theorem.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.195-203
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• 2005

We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.853-862
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• 2014

In this paper, we define a metric induced by the Bergman Kernel and prove a property that the metric has under any biholomorphic mapping.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1401-1409
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• 2016

In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.285-303
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• 2013

The asymptotic expansions of the Bergman kernels on the diagonals near the boundary points of exponentially-flat infinite type for pseudoconvex tube domain in $\mathbb{C}^2$ are obtained.