Description
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.
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Reviews
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)
Book Information
ISBN 9783034896054
Author Mats Andersson
Format Paperback
Page Count 164
Imprint Springer Basel
Publisher Springer Basel
