holomorphically convex
Let be a domain, or alternatively for a more general definition let be an dimensional complex analytic manifold. Further let stand for the set of holomorphic functions on .
Definition.
Let be a compact set. We define the holomorphically of as
The domain is called holomorphically convex if for every compact in , is also compact in . Sometimes this is just abbreviated as holomorph-convex.
Note that when , any domain is holomorphically convex since when for all compact . Also note that this is the same as being a domain of holomorphy.
References
- 1 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title | holomorphically convex |
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Canonical name | HolomorphicallyConvex |
Date of creation | 2013-03-22 15:04:33 |
Last modified on | 2013-03-22 15:04:33 |
Owner | jirka (4157) |
Last modified by | jirka (4157) |
Numerical id | 8 |
Author | jirka (4157) |
Entry type | Definition |
Classification | msc 32E05 |
Synonym | holomorph-convex |
Related topic | PolynomiallyConvexHull |
Related topic | SteinManifold |
Defines | holomorphically convex hull |