Dirichlet series and Hardy spaces

Abstract

[en] The aim of this work is to study Dirichlet series, as well as some of the function spaces that they form. We will see the convergence properties of these series and how they differ from power series, as well as other important properties. We will also study the HardyDirichlet spaces $\mathscr{H}^{\infty}$ and $\mathscr{H}^{2}$. Finally, we will study the relationship between Dirichlet series in these spaces and power series in an infinite number of variables in the poly-torus $\mathbb{T}^{\infty}$ and poly-disk $\mathbb{D}^{\infty}$.