Overview
- The topic of complex convexity is a fascinating blend, exhibiting a profound interplay between geometry, topology and analysis
- Gives the first comprehensive account of the theory, as well as its applications in various areas of mathematics
Part of the book series: Progress in Mathematics (PM, volume 225)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (4 chapters)
Keywords
About this book
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.
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)
Authors and Affiliations
Bibliographic Information
Book Title: Complex Convexity and Analytic Functionals
Authors: Mats Andersson, Ragnar Sigurdsson, Mikael Passare
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-7871-5
Publisher: Birkhäuser Basel
-
eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 2004
Hardcover ISBN: 978-3-7643-2420-9Published: 23 April 2004
Softcover ISBN: 978-3-0348-9605-4Published: 21 October 2012
eBook ISBN: 978-3-0348-7871-5Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XI, 164
Topics: Functional Analysis, Functions of a Complex Variable, Partial Differential Equations, Convex and Discrete Geometry