Holomorphic series expansion of functions of carleman type on the interval $[-1,1]$

Hicham Zoubeir

We characterize the functions of some Carleman classes on the unit interval $[-1,1]$ as sums of holomorphic functions in specific neighborhoods of $[-1,1]$. As an application of our main theorem, we perform an alternative construction of the Dyn'kin's pseudoanalytic extension for these Carleman classes on $[-1,1]$.