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Complex Convexity and Analytic Functionals

  • Mats Andersson
  • Ragnar Sigurdsson
  • Mikael Passare

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

Introduction

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.

Keywords

Pseudoconvexity analytic function differential equation partial differential equation

Authors and affiliations

  • Mats Andersson
    • 1
  • Ragnar Sigurdsson
    • 2
  • Mikael Passare
    • 3
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden
  2. 2.Science InstituteUniversity of IcelandReykjaviíkIceland
  3. 3.Department of MathematicsStockholm UniversityStockholmSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-7871-5
  • Copyright Information Birkhäuser Verlag 2004
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-9605-4
  • Online ISBN 978-3-0348-7871-5
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site