Spaces of Dirichlet series

2019

This work is dedicated to the study of multiple Dirichlet series and it focuses on three main aspects: convergence, spaces of bounded multiple Dirichlet series and the composition operators of such spaces. In the first chapter we give the necessary preliminary results on regular convergence of double and multiple series and its equivalence with the definition of convergence in a restricted sense. We also recall sequences of bounded variation and we show how they are the multipliers of convergent series in the space of sequences, extending also this characterization to double and multiple regularly conergent series. In the second chapter we recall the fundamentals on the theory of bounded or…