Complex Convexity and Analytic Functionals (Paperback)

Mats Andersson

ISBN 10: 3034896050 / ISBN 13: 9783034896054

Published by Springer Basel, Basel, 2012

About this Item

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.

Seller Inventory # 9783034896054

Bibliographic Details

• Title: Complex Convexity and Analytic Functionals (Paperback)
• Publisher: Springer Basel, Basel
• Publication Date: 2012
• Language: English
• ISBN 10: 3034896050
• ISBN 13: 9783034896054
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

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)