03450nam a22004575i 4500 978-0-85729-603-0 DE-He213 20260521092041.0 cr nn 008mamaa 110422s2011 xxk| s |||| 0|eng d 9780857296030 99780857296030 10.1007/978-0-85729-603-0 doi 515.94 23 Pham, Frédéric. author. Singularities of integrals [electronic resource] : Homology, hyperfunctions and microlocal analysis / by Frédéric Pham. London : Springer London, 2011. XI, 217 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Universitext, 0172-5939 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. 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. MATHEMATICS. GEOMETRY, ALGEBRAIC. DIFFERENTIAL EQUATIONS, PARTIAL. MATHEMATICS. SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES. ALGEBRAIC GEOMETRY. APPROXIMATIONS AND EXPANSIONS. SpringerLink (Online service) Springer eBooks Printed edition: 9780857296023 Universitext, 0172-5939 http://dx.doi.org/10.1007/978-0-85729-603-0 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 36006 36006 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.94 2025-10-06 08:44:45 2025-10-06 ER