Hardy spaces of general Dirichlet series - a survey

2019/02/06 by Defant, Andreas, Schoolmann, Ingo
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1902.02073

Abstract

The main purpose of this article is to survey on some key elements of a recent H_p-theory of general Dirichlet series ∑ a_n e^-λ_ns, which was mainly inspired by the work of Bayart and Helson on ordinary Dirichlet series ∑ a_n n^-s. In view of an ingenious identification of Bohr, the H_p-theory of ordinary Dirichlet series can be seen as a sub-theory of Fourier analysis on the infinite dimensional torus \mathbbT^∞. Extending these ideas, the H_p-theory of λ-Dirichlet series is build as a sub-theory of Fourier analysis on what we call λ-Dirichlet groups. A number of problems is added.

Related

• H_p-theory of general Dirichlet series
• Variants of a theorem of Helson on general Dirichlet series
• Some open questions in analysis for Dirichlet series
• Vector-valued general Dirichlet series
• Fréchet spaces of general Dirichlet series