6533b7cefe1ef96bd12572e5

RESEARCH PRODUCT

Dirichlet approximation and universal Dirichlet series

Manuel MaestreFrédéric BayartPaul M. GauthierRichard M. AronVassili Nestoridis

subject

Pure mathematicsMathematics - Complex VariablesUniversal seriesApplied MathematicsGeneral Mathematics010102 general mathematicsMathematics::Analysis of PDEsMathematics::Spectral Theory16. Peace & justice01 natural sciencesDirichlet distributionEuclidean distancesymbols.namesakeChordal graph0103 physical sciencesRight half-planeFOS: Mathematics30K10symbols010307 mathematical physicsComplex Variables (math.CV)0101 mathematicsDirichlet seriesMathematics

description

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 Vitushkin. We also strengthen the notion of universal Dirichlet series.

yearjournalcountryeditionlanguage
2016-08-23Proceedings of the American Mathematical Society
https://doi.org/10.1090/proc/13607