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Singularities of integrals: Homology, hyperfunctions and microlocal analysis (Universitext) by Pham, Frâedâeric is a nonfiction available to read on EtoBox.

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""Contents""; ""Foreword""; ""Part I Introduction to a topological study of Landau singularities""; ""Introduction""; ""I Differentiable manifolds""; ""1 Definition of a topological manifold""; ""2 Structures on a manifold""; ""3 Submanifolds""; ""4 The tangent space of a differentiable manifold""; ""5 Differential forms on a manifold""; ""6 Partitions of unity on a C manifold""; ""7 Orientation of manifolds. Integration on manifolds""; ""8 Appendix on complex analytic sets""; ""II Homology and cohomology of manifolds""; ""1 Chains on a manifold (following de Rham). Stokes' formula"";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

Who reads Singularities of integrals: Homology, hyperfunctions and microlocal analysis (Universitext)?

Author

Pham, Frâedâeric

Publisher

Springer, Springer Science+Business Media

Published

2011

Language

EN

ISBN

9782759803637

Category

nonfiction

Subjects

Mathematics, Science, Physics