Complex Convexity and Analytic Functionals (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
164
Utgivningsdatum
2004-04-01
Upplaga
2004 ed.
Förlag
Birkhauser Verlag AG
Medarbetare
Passare, Mikael
Illustrationer
XI, 164 p.
Volymtitel
v. 225
Dimensioner
235 x 160 x 15 mm
Vikt
420 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9783764324209

Complex Convexity and Analytic Functionals

av Mats Andersson, Mikael Passare, Ragnar Sigurdsson
Inbunden,  Engelska, 2004-04-01
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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 Andr 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 Fantappi transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.
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Mats Andersson, Mikael Passare, Ragnar Sigurdsson

Recensioner i media

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)

Innehållsförteckning

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 Fantappi 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 Fantappi 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.

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