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

## 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