Interactions between methods of local Banach space theory and infinite dimensional complex analysis

大约在1914年，玻尔发表了关于狄利克雷级数理论的基本文章，并在解析数论和复分析之间建立了密切的关系。特别是玻尔幂级数定理，近年来激发了一系列有趣的论文，给现代巴拿赫空间理论，即所谓的局部理论与无限维复分析意想不到的强联系带来了希望。从目前的研究水平和我们的准备工作来看，局部巴拿赫空间理论和复分析之间的富有成效的相互作用已经结晶。我们项目的首要目标是更好地理解这种关系。这包括与数论、组合学、概率论和复流形上的偏微分方程理论的联系。

About 1914 H. Bohr published fundamental articles on the theory of Dirichlet series and created a close relationship between analytic number theory and complex analysis. In particular, Bohr¿s power series theorem has stimulated a series of interesting papers in recent years, which gives hope to an unexpected strong connection of modern Banach space theory, the so-called local theory, with infinite dimensional complex analysis. From the present state-of¿the-art of research and our preparatory work, a fruitful interaction between local Banach space theory and complex analysis has crystallized. The top aim of our project is to get a better understanding of this relationship. This includes connections with number theory, combinatorics, probability theory and the theory of partial differential equations on complex manifolds.