Singularities of integrals

Homology, hyperfunctions and microlocal analysis

Authors:

ISBN: 978-0-85729-602-3 (Print) 978-0-85729-603-0 (Online)

Table of contents (14 chapters)

  1. Front Matter

    Pages I-XI

  2. Introduction to a topological study of Landau singularities

    1. Front Matter

      Pages 1-5

    2. No Access

      Book Chapter

      Pages 7-28

      Differentiable manifolds

    3. No Access

      Book Chapter

      Pages 29-53

      Homology and cohomology of manifolds

    4. No Access

      Book Chapter

      Pages 55-65

      Leray’s theory of residues

    5. No Access

      Book Chapter

      Pages 67-83

      Thom’s isotopy theorem

    6. No Access

      Book Chapter

      Pages 85-108

      Ramification around Landau varieties

    7. No Access

      Book Chapter

      Pages 109-126

      Analyticity of an integral depending on a parameter

    8. No Access

      Book Chapter

      Pages 127-136

      Ramification of an integral whose integrand is itself ramified

    9. Back Matter

      Pages 137-144

  3. Introduction to the study of singular integrals and hyperfunctions

    1. Front Matter

      Pages 145-148

    2. No Access

      Book Chapter

      Pages 149-156

      Functions of a complex variable in the Nilsson class

    3. No Access

      Book Chapter

      Pages 157-162

      Functions in the Nilsson class on a complex analytic manifold

    4. No Access

      Book Chapter

      Pages 163-169

      Analyticity of integrals depending on parameters

    5. No Access

      Book Chapter

      Pages 171-174

      Sketch of a proof of Nilsson’s theorem

    6. No Access

      Book Chapter

      Pages 175-184

      Examples: how to analyze integrals with singular integrands

    7. No Access

      Book Chapter

      Pages 185-190

      Hyperfunctions in one variable, hyperfunctions in the Nilsson class

    8. No Access

      Book Chapter

      Pages 191-200

      Introduction to Sato’s microlocal analysis

  4. Back Matter

    Pages 201-217