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

摘要

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 ] .