© 2004

Complex Convexity and Analytic Functionals


Part of the Progress in Mathematics book series (PM, volume 225)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Mats Andersson, Ragnar Sigurdsson, Mikael Passare
    Pages 1-13
  3. Mats Andersson, Ragnar Sigurdsson, Mikael Passare
    Pages 15-72
  4. Mats Andersson, Ragnar Sigurdsson, Mikael Passare
    Pages 73-128
  5. Mats Andersson, Ragnar Sigurdsson, Mikael Passare
    Pages 129-150
  6. Back Matter
    Pages 151-164

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.


Pseudoconvexity analytic function differential equation partial differential equation

Authors and affiliations

  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden
  2. 2.Science InstituteUniversity of IcelandReykjaviíkIceland
  3. 3.Department of MathematicsStockholm UniversityStockholmSweden

Bibliographic information

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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)