THE COEFFICIENTS OF BELL DOMAINS AND THE CRITICAL POINTS OF CORRESPONDING FUNCTIONS

  • Jeong, Moonja (Department of Mathematics The University of Suwon)
  • Received : 2008.08.24
  • Published : 2009.12.30

Abstract

In this note, we determine the properties of the coefficients of Bell domains in the plane and find some coefficients to consist of Bell domain.

Keywords

References

  1. S. Bell, Complex of the classical kernel functions of potential theory, Indiana Univ. Math. J., 44 (1995), 1337-1369.
  2. S. Bell, Finitely generated function fields and complexity in potential theory in the plane, Duke Math. J., 98 (1999), 187-207. https://doi.org/10.1215/S0012-7094-99-09805-8
  3. S. Bell, A Riemann surface attached to domains in the plane and complexity in potential theory, Houston J. Math., 26 (2000), 277-297.
  4. L. R. Goldberg, Catalan numbers and branched coverings by the Riemann sphere, Adv. in Math. 85. (1991), 129-144. https://doi.org/10.1016/0001-8708(91)90052-9
  5. I. P. Goulden and D. M. Jackson, Transitive factorisation into transpositions and holomorphic mappings on the sphere, Proc. AMS 125. (1997), 51-60. https://doi.org/10.1090/S0002-9939-97-03880-X
  6. M. Jeong and M. Taniguchi, Bell representation of finitely connected planar domains, Proc. AMS., 131 (2003), 2325-2328. https://doi.org/10.1090/S0002-9939-02-06823-5
  7. M. Jeong and M. Taniguchi, Algebraic kernel functions and representation of planar domains, J. Korean Math. Soc., 40 (2003), 447-460. https://doi.org/10.4134/JKMS.2003.40.3.447
  8. M. Jeong and M. Taniguchi, The cofficient body of Bell representations of finitely connected planar domains, J. Math. Anal. Appl. 295 (2004), 620-632. https://doi.org/10.1016/j.jmaa.2004.03.043