JournalszaaVol. 13, No. 2pp. 307–327

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
On the Existence of Holomorphic Functions Having Prescribed Asymptotic Expansions cover
Download PDF

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 DD of the boundary Ω\partial \Omega of a domain Ω\Omega of CC has no accumulation point and if the connected component in Ω\partial \Omega of every is uDu \in D has more than one point, then DD is regularly asymptotic for Ω\Omega, i.e. for every family {cu,n:uD,nN0c_{u,n}: u \in D, n \in \mathbb N_0} of complex numbers, there is a holomorphic function ff on Ω\Omega which at every uDu \in D has n=0cu,n(zu)n\sum^{\infty}_{n=0} c_{u,n} (z–u)^n as asymptotic expansion at uu.

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