Complex Convexity and Analytic Functionals
A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes. These notions are intermediates between ordinary geometric convexity and pseudoconvexity. Their...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
2004, 2004
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| Edition: | 1st ed. 2004 |
| Series: | Progress in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Convexity in Real Projective Space
- 1.1 Convexity in real affine space
- 1.2 Real projective space
- 1.3 Convexity in real projective space
- 2 Complex Convexity
- 2.1 Linearly convex sets
- 2.2 ?-convexity: Definition and examples
- 2.3 ?-convexity: Duality and invariance
- 2.4 Open ?-convex sets
- 2.5 Boundary properties of ?-convex sets
- 2.6 Spirally connected sets
- 3 Analytic Functionals and the Fantappiè Transformation
- 3.1 The basic pairing in affine space
- 3.2 The basic pairing in projective space
- 3.3 Analytic functionals in affine space
- 3.4 Analytic functionals in projective space
- 3.5 The Fantappiè transformation
- 3.6 Decomposition into partial fractions
- 3.7 Complex Kergin interpolation
- 4 Analytic Solutions to Partial Differential Equations
- 4.1 Solvability in ?-convex sets
- 4.2 Solvability and P-convexity for carriers
- References