ℂ-convexity in infinite-dimensional banach spaces and applications to kergin interpolation
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ID: 148794
2006
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Abstract
We investigate the concepts of linear convexity and ℂ-convexity
in complex Banach spaces. The main result is that any
ℂ-convex domain is necessarily linearly convex. This is a
complex version of the Hahn-Banach theorem, since it means the
following: given a ℂ-convex domain Ω
in the Banach space
X
and a point p∉Ω, there is a complex hyperplane
through p
that does not intersect Ω. We also prove that
linearly convex domains are holomorphically convex, and that
Kergin interpolation can be performed on holomorphic mappings
defined in ℂ-convex domains.
| Reference Key |
filipsson2006international-convexity
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|---|---|
| Authors | ;Lars Filipsson |
| Journal | structural engineering and mechanics |
| Year | 2006 |
| DOI |
10.1155/IJMMS/2006/80846
|
| URL | |
| Keywords |
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