Envelopes of holomorphy of Hartogs and circular domains

A Schlichtness Theorem for Envelopes of Holomorphy

Let Ω be a domain in C. We prove the following theorem. If the envelope of holomorphy of Ω is schlicht over Ω, then the envelope is in fact schlicht. We provide examples showing that the conclusion of the theorem does not hold in Cn, n > 2. Additionally, we show that the theorem cannot be generalized to provide information about domains in C whose envelopes are multiply sheeted.

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

Normed Domains of Holomorphy

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 will use the following notation: D denotes the unit disc in the complex plane. We let D2 D × D denote the bidisc, and D D × D × · · · × D the polydisc in C. The symbol B Bn is the unit ball in C. A domainΩ ⊆ C is said to be Runge if any holomorphic f onΩ is the limit, uniformly ...

Envelopes of Holomorphy and Extension of Functions of Bounded Type

In this article we characterize the envelope of holomorphy for the algebra of bounded type holomorphic functions on Riemann domains over a Banach space in terms of the spectrum of the algebra. We prove that evaluations at points of the envelope are always continuous but we show an example of a balanced open subset of c0 where the extensions to the envelope are not necessarily of bounded type, a...

Lineally convex Hartogs domains

We study lineally convex domains of a special type, viz. Hartogs domains, and prove that such sets can be characterized by local conditions if they are smoothly bounded.