Dirichlet approximation and universal Dirichlet series
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- by Richard M. Aron, Frédéric Bayart, Paul M. Gauthier, Manuel Maestre and Vassili Nestoridis PDF
- Proc. Amer. Math. Soc. 145 (2017), 4449-4464 Request permission
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.References
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Additional Information
- Richard M. Aron
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- MR Author ID: 27325
- Email: aron@math.kent.edu
- Frédéric Bayart
- Affiliation: Laboratoire de Mathématiques, Université Blaise Pascal, BP 10448, F-63000 Clermont-Ferrand, France
- MR Author ID: 683115
- 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
- MR Author ID: 130365
- Email: vnestor@math.uoa.gr
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4449-4464
- MSC (2010): Primary 30K10; Secondary 46G20, 30E10
- DOI: https://doi.org/10.1090/proc/13607
- MathSciNet review: 3690628