• 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.

• 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.

• 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.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.105-113
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• 1999

Suppose that ${\Omega}$ is a bounded domain with $C^{\infty}$ smooth boundary in the plane whose associated Bergman kernel, exact Bergman kernel, or $Szeg{\ddot{o}}$ kernel function is an algebraic function. We shall prove that any proper holomorphic mapping of ${\Omega}$ onto the unit disc is algebraic.