• 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.

• 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.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.425-437
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• 2002

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^{n}$ and let $z^{0}$ $\in$b$\Omega$ a point of finite type. We also assume that the Levi form of b$\Omega$ is comparable in a neighborhood of $z^{0}$ . Then we get precise estimates of the Bergman kernel function, $K_{\Omega}$(z, w), and its derivatives in a neighborhood of $z^{0}$ . .

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.349-355
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• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• 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.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.447-460
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• 2003

In this paper we study the non-degenerate n-connected canonical domains with n>1 related to the conjecture of S. Bell in [4]. They are connected to the algebraic property of the Bergman kernel and the Szego kernel. We characterize the non-degenerate doubly connected canonical domains.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.777-786
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• 2014

We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the or-thonormal basis for the Hardy space consisting of the Szegő kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.