Complex Convexity and Analytic Functionals
By: by Mats Andersson, Ragnar Sigurdsson, Mikael Passare
Contributors: Sigurdsson, Ragnar; Passare, Mikael
Series: Progress in Mathematics -- 225; Progress in Mathematics -- 225
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2004
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 164
ISBN-13: 9783034896054; 9783034878715
Subjects: Functional analysis; Mathematics; Functions of complex variables; Discrete groups; Partial Differential equations
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 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.
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Table of contents: title: Introduction; title: 1. Convexity in Real Projective Space; title: 2. Complex Convexity; title: 3. Analytic Functionals and the Fantappié Transformation; title: 4. Analytic Solutions to Partial Differential Equations; title: References.