Detailansicht
Complex Convexity and Analytic Functionals
Progress in Mathematics 225
ISBN/EAN: 9783764324209
Umbreit-Nr.: 967064
Sprache:
Englisch
Umfang: xi, 164 S.
Format in cm:
Einband:
gebundenes Buch
Erschienen am 23.04.2004
- Zusatztext
- InhaltsangabeIntroduction.- 1. Convexity in Real Projective Space.- 2. Complex Convexity.- 3. Analytic Functionals and the Fantappié Transformation.- 4. Analytic Solutions to Partial Differential Equations.- References.
- Kurztext
- The topic of complex convexity is a fascinating blend, exhibiting a profound interplay between geometry, topology and analysisGives the first comprehensive account of the theory, as well as its applications in various areas of mathematics
- Autorenportrait
- Inhaltsangabe1 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.