Smooth Universal Taylor Series

• Autores: Ch. Kariofillis, Ch. Konstadilaki, Vassili Nestoridis
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 147, Nº 3, 2006, págs. 249-257
• Idioma: inglés
• DOI: 10.1007/s00605-005-0323-2
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• Resumen

  • 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