Holomorphic series expansion of functions of Carleman type on the interval [−1, 1]

Abstract

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].