• Title, Summary, Keyword: Bergman Kernel

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THE RELATION BETWEEN THE BERGMAN KERNEL AND THE SZEGO KERNEL

  • Jeong, Moon-Ja
    • 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.

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THE BERGMAN KERNEL FUNCTION AND THE SZEGO KERNEL FUNCTION

  • CHUNG YOUNG-BOK
    • 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.

THE BERGMAN KERNEL FUNCTION AND THE DENSITY THEOREMS IN THE PLANE

  • Jeong, Moonja
    • 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.

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THE EXACT BERGMAN KERNEL AND THE EXTREMAL PROBLEM

  • Jeong, Moonja
    • 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.

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CONFORMAL MAPPING AND CLASSICAL KERNEL FUNCTIONS

  • CHUNG, YOUNG-BOK
    • 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.

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ON THE TRANSFORMATION FORMULA OF THE SLICE BERGMAN KERNELS IN THE QUATERNION VARIABLES

  • Park, Jong-Do
    • 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.