Resumen de Smooth Universal Taylor Series

Ch. Kariofillis, Ch. Konstadilaki, Vassili Nestoridis

• Let be a simply connected domain in , such that is connected. If g is holomorphic in O and every derivative of g extends continuously on , then we write g ? A8 (O). For g ? A8 (O) and we denote . We prove the existence of a function f ? A8(O), such that the following hold: i) There exists a strictly increasing sequence µn ? {0, 1, 2, ¿}, n = 1, 2, ¿, such that, for every pair of compact sets G, ? ? and every l ? {0, 1, 2, ¿} we have ii) For every compact set with and Kc connected and every function continuous on K and holomorphic in K0, there exists a subsequence of , such that, for every compact set we have