Journal d'Analyse Mathématique

, Volume 135, Issue 1, pp 225–247 | Cite as

Almost sure-sign convergence of Hardy-type Dirichlet series

  • Daniel CarandoEmail author
  • Andreas Defant
  • Pablo Sevilla-Peris


Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series \(\sum\nolimits_n {{a_n}{n^{ - s}}} \) is uniformly a.s.- sign convergent (i.e., \(\sum\nolimits_n {{\varepsilon _n}{a_n}{n^{ - s}}} \) converges uniformly for almost all sequences of signs εn = ±1) but does not convergent absolutely, equals 1/2. We study this result from a more modern point of view within the framework of so-called Hardytype Dirichlet series with values in a Banach space


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Copyright information

© Hebrew University Magnes Press 2018

Authors and Affiliations

  • Daniel Carando
    • 1
    • 2
    Email author
  • Andreas Defant
    • 3
  • Pablo Sevilla-Peris
    • 4
  1. 1.Departamento de Matematica - Pab I, Facultad de Cs. Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.IMAS - CONICETBuenos AiresArgentina
  3. 3.Institut für MathematikUniversität OldenburgOldenburgGermany
  4. 4.Instituto Universitario de Matem ática Pura y AplicadaUniversitat Politècnica de ValènciaValenciaSpain

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