• Korean Journal of Mathematics
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• 제13권2호
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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.

• 호남수학학술지
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• 제27권2호
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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.

• 대한수학회지
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• 제43권1호
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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.

• 호남수학학술지
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• 제21권1호
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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.