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Field name	Details
Dewey Class	515.94
Title	Singularities of integrals ([Ebook]) : Homology, hyperfunctions and microlocal analysis / by Frédéric Pham.
Author	Pham, Frederic
Other name(s)	SpringerLink (Online service)
Publication	London : Springer London , 2011.
Physical Details	XI, 217 pages : online resource.
Series	Universitext 0172-5939
ISBN	9780857296030
Summary Note	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. Thomâs 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 âmust-haveâ 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.:
Contents note	Differentiable manifolds -- Homology and cohomology of manifolds -- Lerayâs theory of residues -- Thomâs 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 Nilssonâs theorem -- Examples: how to analyze integrals with singular integrands -- Hyperfunctions in one variable, hyperfunctions in the Nilsson class -- Introduction to Satoâs microlocal analysis.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-0-85729-603-0
Links to Related Works	Subject References: Algebraic Geometry . Approximations and Expansions . Differential equations, Partial . Geometry, Algebraic . Mathematics . Several Complex Variables and Analytic Spaces . Authors: Pham, Frederic . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 515.94 . 515.94 (DDC 23) .

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Singularities of integrals: Homology, hyperfunctions and microlocal analysis

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