000			03469nam a22004695i 4500
001			978-0-85729-603-0
003			DE-He213
005			20140220083714.0
007			cr nn 008mamaa
008			110422s2011 xxk| s |||| 0|eng d
020			_a9780857296030 _9978-0-85729-603-0
024	7		_a10.1007/978-0-85729-603-0 _2doi
050		4	_aQA331.7
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.94 _223
100	1		_aPham, Frédéric. _eauthor.
245	1	0	_aSingularities of integrals _h[electronic resource] : _bHomology, hyperfunctions and microlocal analysis / _cby Frédéric Pham.
264		1	_aLondon : _bSpringer London, _c2011.
300			_aXI, 217 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_aDifferentiable 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.
520			_aBringing 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.
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aApproximations and Expansions.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780857296023
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-85729-603-0
912			_aZDB-2-SMA
999			_c105236 _d105236