International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 12, Article ID 37014, 11 pages
doi:10.1155/IJMMS/2006/37014

Universal approximation theorem for Dirichlet series

Abstract

The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in comparing both results. Several density results are proved that finally lead to the main theorem on simultaneous approximation.