On the Existence of Holomorphic Functions Having Prescribed Asymptotic Expansions

  • M. Valdivia

    Universidad de Valencia, Burjasot (Valencia), Spain
  • Jean Schmets

    CHU Sart Tilman, Liège, Belgium

Abstract

A generalization of some results of T. Carleman in [1] is developped. The practical form of it states that if the non-empty subset of the boundary of a domain of has no accumulation point and if the connected component in of every is has more than one point, then is regularly asymptotic for , i.e. for every family {} of complex numbers, there is a holomorphic function on which at every has as asymptotic expansion at .

Cite this article

M. Valdivia, Jean Schmets, On the Existence of Holomorphic Functions Having Prescribed Asymptotic Expansions. Z. Anal. Anwend. 13 (1994), no. 2, pp. 307–327

DOI 10.4171/ZAA/511