Articoli correlati a Complex Convexity and Analytic Functionals: 225
Sinossi
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.
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Recensione
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“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)
Contenuti
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.
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Complex Convexity and Analytic Functionals (Progress in Mathematics)
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Paperback. Condizione: new. Paperback. 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 Andre 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 Fantappie transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9783034896054
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Complex Convexity and Analytic Functionals (Progress in Mathematics)
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Complex Convexity and Analytic Functionals (Progress in Mathematics)
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Complex Convexity and Analytic Functionals (Progress in Mathematics)
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Complex Convexity and Analytic Functionals
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Birkhäuser Basel, Springer Okt 2012, 2012
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 180 pp. Englisch. Codice articolo 9783034896054
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Complex Convexity and Analytic Functionals
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