Complex Convexity and Analytic Functionals

Mats Andersson

ISBN 10: 3764324201 / ISBN 13: 9783764324209

Published by Birkhäuser Basel, Birkhäuser Basel Apr 2004, 2004

About this Item

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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 180 pp. Englisch.

Seller Inventory # 9783764324209

Bibliographic Details

• Title: Complex Convexity and Analytic Functionals
• Publisher: Birkhäuser Basel, Birkhäuser Basel Apr 2004
• Publication Date: 2004
• Language: English
• ISBN 10: 3764324201
• ISBN 13: 9783764324209
• Binding: Buch
• Condition: Neu

About this title

Synopsis

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.

Review

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)