Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables
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Andreas Defant
Abstract
Let ℱ(R) be a set of holomorphic functions on a Reinhardt domain R in a Banach sequence space (as e.g. all holomorphic functions or all m-homogeneous polynomials on the open unit ball of 
). We give a systematic study of the sets dom ℱ(R) of all z ∈ R for which the monomial expansion 
of every ƒ ∈ ℱ(R) converges. Our results are based on and improve the former work of Bohr, Dineen, Lempert, Matos and Ryan. In particular, we show that 
up to any ε > 0 is the unique Banach sequence space X for which the monomial expansion of each holomorphic function ƒ converges at each point of a given Reinhardt domain in X. Our study shows clearly why Hilbert's point of view to develop a theory of infinite dimensional complex analysis based on the concept of monomial expansion, had to be abandoned early in the development of the theory.
© Walter de Gruyter Berlin · New York 2009
Articles in the same Issue
- On the stable trace formula for Sp4
- Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables
- Deformation theory of representations of prop(erad)s I
- Normes invariantes et existence de filtrations admissibles
- Relaxation of the flow of triods by curve shortening flow via the vector-valued parabolic Allen-Cahn equation
- Construction of type II1 factors with prescribed countable fundamental group
- Prym-Tyurin varieties via Hecke algebras
Articles in the same Issue
- On the stable trace formula for Sp4
- Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables
- Deformation theory of representations of prop(erad)s I
- Normes invariantes et existence de filtrations admissibles
- Relaxation of the flow of triods by curve shortening flow via the vector-valued parabolic Allen-Cahn equation
- Construction of type II1 factors with prescribed countable fundamental group
- Prym-Tyurin varieties via Hecke algebras
