Vector-valued general Dirichlet series
Volume 258 / 2021
Studia Mathematica 258 (2021), 269-316
MSC: Primary 30B50, 43A70, 43A17, 46E40.
DOI: 10.4064/sm200127-24-4
Published online: 4 December 2020
Abstract
With early contributions due to, among others, Besicovitch, Bohr, Bohnenblust, Hardy, Hille, Riesz, Neder and Landau, the last 20 years show a substantial revival of systematic research on ordinary Dirichlet series $\sum a_n n^{-s}$, and more recently even on general Dirichlet series $\sum a_n e^{-\lambda _n s}$. This involves the intertwining of classical work with modern functional analysis, harmonic analysis, infinite-dimensional holomorphy and probability theory as well as analytic number theory. The main goal of this article is to start a systematic study of a variety of fundamental aspects of vector-valued general Dirichlet series $\sum a_n e^{-\lambda _{n} s}$, where the coefficients are in an arbitrary Banach space $X$.
