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

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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.