Singularities of integrals Homology, hyperfunctions and microlocal analysis /

• Main Author: Pham, Frédéric (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2011.
• Series: Universitext,
• Subjects: Mathematics.; Algebraic geometry.; Approximation theory.; Functions of complex variables.; Several Complex Variables and Analytic Spaces.; Algebraic Geometry.; Approximations and Expansions.

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 variable...

Table of Contents:

• Differentiable manifolds
• Homology and cohomology of manifolds
• Leray’s theory of residues
• Thom’s isotopy theorem
• Ramification around Landau varieties
• Analyticity of an integral depending on a parameter
• Ramification of an integral whose integrand is itself ramified
• Functions of a complex variable in the Nilsson class
• Functions in the Nilsson class on a complex analytic manifold
• Analyticity of integrals depending on parameters
• Sketch of a proof of Nilsson’s theorem
• Examples: how to analyze integrals with singular integrands
• Hyperfunctions in one variable, hyperfunctions in the Nilsson class
• Introduction to Sato’s microlocal analysis.