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Complex Convexity and Analytic Functionals : Progress in Mathematics - Mats Andersson

Complex Convexity and Analytic Functionals

Progress in Mathematics


Published: 1st June 2004
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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 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.

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)

Convexity in real projective space
Complex convexity
Analytic functionals and the Fantappie transformation
Analytic solutions to partial differential equations
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764324209
ISBN-10: 3764324201
Series: Progress in Mathematics : Book 225
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 164
Published: 1st June 2004
Country of Publication: CH
Dimensions (cm): 23.39 x 15.6  x 1.12
Weight (kg): 0.43