Normed Domains of Holomorphy

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We treat the classical concept of domain of holomorphy in C when the holomorphic functions considered are restricted to lie in some Banach space. Positive and negative results are presented. A new view of the case n = 1 is considered. 0 Introduction In this paper a domain Ω ⊆ C is a connected open set. We let O(Ω) denote the algebra of holomorphic functions on Ω. We shall use the following nota...

Domains of Holomorphy with Edges and Lower Dimensional Boundary Singularities

Necessary and sufficient geometric conditions are given for domains with regular boundary points and edges to be domains of holomorphy provided the remainder boundary subset is of zero Hausdorff 1-codimensional measure.

The Envelope of Holomorphy of Riemann Domains over a Countable Product of Complex Planes

This paper deals with the problem of constructing envelopes of holomorphy for Riemann domains over a locally convex space. When this locally convex space is a countable product of complex planes the existence of the envelope of holomorphy is proved and the domains of holomorphy are characterized. For the Riemann domains over the cartesian product CN of a countable number of complex planes, the ...

On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle

Domains of existence of polymonogenic functions

A domain is called domain of holomorphy if it is so for a function f: The domain is called non-extensible to a boundary point a; if there exists a neighborhood U of a; an open set V U \ and a holomorphic function g : V ! C that has no holomorphic extension to the point a: Any domain of holomorphy is non-extensible to any boundary point. Levi’s problem (1910): If the inverse is true, that is, an...