Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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CONFORMAL MAPPING AND CLASSICAL KERNEL FUNCTIONS

  • CHUNG, YOUNG-BOK (Department of Mathematics Chonnam National University)
  • Received : 2005.05.01
  • Accepted : 2005.06.01
  • Published : 2005.06.25
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Abstract

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.

Keywords

Acknowledgement

Supported by : Chonnam National University

References

  1. Complex Variables Theory Appl. v.29 no.4 Recipes for classical kernel functions associated to a multiply connected domain in the plane Bell, S.
  2. Duke Math. J. v.64 no.1 The Szego projection and the classical objects of potential theory in the plane Bell, Steve
  3. The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics Bell, Steven R.
  4. Indiana Univ. Math. J. v.44 no.4 Complexity of the classical kernel functions of potential theory Bell, Steven R.
  5. The kernel function and conformal mapping;Mathematical Surveys, No. V Bergman, Stefan
  6. Indiana Univ. Math. J. v.42 The Bergman kernel function and the Ahlfors mapping in the plane Chung, Y.B.
  7. J. Math. Pures Appl. v.75 An expression of the Bergman kernel function in terms of the Szego kernel Chung, Y.B.
  8. Trans. Amer. Math. Soc. v.67 Schwarz's lemma and the Szego kernel function Garabedian, P.R.
  9. Math. Ann. v.236 The Cauchy kernel, the Szego kernel, and the Riemann mapping function Kerzman, N.;Stein, E.M.
  10. Numerical conformal mapping via the Szego kernel;Numerical conformal mapping Kerzman, N.;Trummer, M.;Trefethen(ed.)
  11. Pitman Research Notes in Mathematics Series v.189 Theory of reproducing kernels and its applications Saitoh, Saburou
  12. Duke Math. J. v.17 Various types of orthogonalization Schiffer, Menahem
  13. SIAM J. Numer. Anal. v.23 An efficient implementation of a conformal mapping method based on the Szego kernel Trummer, M.