• CHUNG, YOUNG-BOK (Dept. of Mathematics, Chonnam National University)
  • Received : 1999.02.04
  • Published : 1999.07.30


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.



Supported by : GARC


  1. Approximation theorem on mapping properties of the classical kernel functions of complex analysis Jeong, M.
  2. Function Theory in the Unit Ball of $C^n& , Grudlehren der Mathematischen Wisswnschaften in Einzeldarstellungen Rudin, W.
  3. Several Complex Variables Bochner, S.;Martin, W.
  4. Indiana Univ. Math. J. v.42 no.4 The Bergman Kernel Function and the Ahlfors Mapping in the Plane Chung, Y.B.
  5. Journal de Mathematiques Pures et Appliquees v.75 An expression of the Bergman kernel function in terms of the Szego kernel Chung, Y.B.
  6. Tran Amer. Math. Soc. v.270 The Bergman kernel function and proper holomorphic mappings Bell, S.
  7. Trans. Amer. Math. Soc. v.284 Proper holomorphic mappings that must be rational Bell, S.
  8. RIM-GARC preprint series v.37 A computation of the exact Bergman kernel function Chung, Y.B.