Singularities of integrals

Homology, hyperfunctions and microlocal analysis

  • Frédéric Pham

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Introduction to a topological study of Landau singularities

    1. Front Matter
      Pages 1-5
    2. Frédéric Pham
      Pages 7-28
    3. Frédéric Pham
      Pages 29-53
    4. Frédéric Pham
      Pages 55-65
    5. Frédéric Pham
      Pages 67-83
    6. Frédéric Pham
      Pages 85-108
    7. Back Matter
      Pages 137-144
  3. Introduction to the study of singular integrals and hyperfunctions

  4. Back Matter
    Pages 201-217

About this book

Introduction

Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis.

Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered.

This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals.

Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.

Keywords

Homology Landau variety Leray residue Picard-Lefschetz formulae boundary value current family of supports functions in the Nilsson class hyperfunctions hyperfunctions in the Nilsson class microsupport residue theorem singularity of integrals depending on parameters

Authors and affiliations

  • Frédéric Pham
    • 1
  1. 1.Laboratoire J.-A. DieudonnéUniversité de Nice Sophia AntipolisNice cedex 02France

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-603-0
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-602-3
  • Online ISBN 978-0-85729-603-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book