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Advances in Complex Function Theory (Lecture Notes in Mathematics) by W. E. Kirwan (Repost)
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Complex Convexity and Analytic Functionals (Progress in Mathematics)
Posted on 2010-04-15
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Author: Ragnar Sigurdsson, Mikael Passare, Mats Andersson
Publisher: Birkh?user Basel (2004) Binding: Hardcover, 160 pages pricer: $119.00 ISBN-10: 3764324201 editorialreviews 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 Andr¨¦ 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 Fantappi¨¦ transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations. checked checked
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