Complex Convexity and Analytic Functionals
(Sprache: Englisch)
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...
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Klappentext zu „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 importance was first manifested in the pioneering work of André Martineau from about forty years ago. Since then a large number of new related results have been obtained by many different mathematicians. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.
Inhaltsverzeichnis zu „Complex Convexity and Analytic Functionals “
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.
Autoren-Porträt von Mats Andersson, Mikael Passare, Ragnar Sigurdsson
The topic of complex convexity is a fascinating blend, exhibiting a profound interplay between geometry, topology and analysis. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappiè transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.Bibliographische Angaben
- Autoren: Mats Andersson , Mikael Passare , Ragnar Sigurdsson
- 2012, XI, 164 Seiten, Maße: 16 x 23,3 cm, Kartoniert (TB), Englisch
- Verlag: Birkhäuser
- ISBN-10: 3034896050
- ISBN-13: 9783034896054
Sprache:
Englisch
Pressezitat
From the reviews: "This valuable monograph, which was in preparation for a decade, ... The book consists of four chapters, each of which begins with a helpful summary and concludes with bibliographic references and historical comments."(ZENTRALBLATT MATH)
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