Domains of convergence in infinite dimensional holomorphy

For certain subsets F(R) of holomorphic functions on a Reinhardt domain R in a Banach sequence space X, mainly for H_{\infty}(R), P^m(X) and P(X), we give precise descriptions of the domain of convergence dom F(R), i.e. the set of all points of R where the monomial expansion \sum_{\alpha\in \N_0^{(\N)}} \frac{\partial^{\alpha} f (0)}{\alpha !} z^{\alpha} of every function f \in F(R) is (unconditionally) convergent. The results are obtained by an interplay of complex analysis and local Banach space theory, improving work of Ryan and Lempert about monomial expansions of holomorphic functions on \ell_1 and using methods from the theory of multidimensional Bohr radii. The problem of conditional convergence is solved for polynomials. It is closely connected with bases for full and symmetric tensor products and convergence preserving permutations.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Oldenburg

Year

2005

Author dc:creator

• Prengel, Christopher

• [Keine Schlagwörter von Autor/in vergeben.]

Repository record source_url

http://oops.uni-oldenburg.de/91

OAI identifier oai:identifier

oai:oops.uni-oldenburg.de:91