Almost sure-sign convergence of Hardy-type Dirichlet series

2014/12/16 by Carando, Daniel, Defant, Andreas, Sevilla-Peris, Pablo
#30B50 #30H10 #46G20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1412.5030

Abstract

Hartman proved in 1939 that the width of the largest possible strip in the complex plane, on which a Dirichlet series ∑_n a_n n^-s is uniformly a.s.-sign convergent (i.e., ∑_n ε_n a_n n^-s converges uniformly for almost all sequences of signs ε_n =± 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 Hardy-type Dirichlet series with values in a Banach space.

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