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Universal approximation theorem for Dirichlet series

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  • O. Demanze
  • A. Mouze

Abstract

The paper deals with an extension theorem by Costakis and Vlachouon 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 simultaneousapproximation.

Suggested Citation

  • O. Demanze & A. Mouze, 2006. "Universal approximation theorem for Dirichlet series," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-11, August.
    • Handle: RePEc:hin:jijmms:037014
    DOI: 10.1155/IJMMS/2006/37014
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