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Dirichlet approximation and universal Dirichlet series


Authors: Richard M. Aron, Frédéric Bayart, Paul M. Gauthier, Manuel Maestre and Vassili Nestoridis
Journal: Proc. Amer. Math. Soc. 145 (2017), 4449-4464
MSC (2010): Primary 30K10; Secondary 46G20, 30E10
DOI: https://doi.org/10.1090/proc/13607
Published electronically: June 8, 2017
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Abstract: We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and to the chordal one as well, analogous to classical results of Runge, Mergelyan and Vituškin. We also strengthen the notion of universal Dirichlet series.


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Additional Information

Richard M. Aron
Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email: aron@math.kent.edu

Frédéric Bayart
Affiliation: Laboratoire de Mathématiques, Université Blaise Pascal, BP 10448, F-63000 Clermont-Ferrand, France
Email: Frederic.Bayart@math.univ-bpclermont.fr

Paul M. Gauthier
Affiliation: Département de mathématiques et de statistique, Université de Montréal, Montréal, Quebec, Canada H3C3J7
Email: gauthier@dms.umontreal.ca

Manuel Maestre
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain
Email: manuel.maestre@uv.es

Vassili Nestoridis
Affiliation: Department of Mathematics, University of Athens, 157 84 Panepistemiopolis, Athens, Greece
Email: vnestor@math.uoa.gr

DOI: https://doi.org/10.1090/proc/13607
Keywords: Universal series, Runge theorem
Received by editor(s): August 28, 2016
Received by editor(s) in revised form: November 22, 2016
Published electronically: June 8, 2017
Additional Notes: Partially supported by the “SQuaREs” program at the American Institute of Mathematics, Palo Alto and the “Research in Pairs” program at the Mathematisches Forshungsinstitut, Oberwolfach.
The first and fourth authors were supported by MINECO and FEDER MTM2014-57838-C2-2-P and Prometeo II/2013/013. The third author was supported by NSERC and Entente France-Québec.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2017 American Mathematical Society