International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 37014, 11 pages
doi:10.1155/IJMMS/2006/37014
Universal approximation theorem for Dirichlet series
1Laboratoire de Mathématiques, UMR 8524, Université des Sciences et Technologies de Lille 1 (USTL), Cité Scientifique, Villeneuve d'Ascq 59650, France
2École Centrale de Lille, Cite Scientifique, BP 48, Villeneuve d'Ascq Cedex 59651, France
Received 14 September 2005; Revised 11 May 2006; Accepted 30 May 2006
Copyright © 2006 O. Demanze and A. Mouze. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.