000			03868nam a22005295i 4500
001			978-3-319-29075-1
003			DE-He213
005			20190213151602.0
007			cr nn 008mamaa
008			160628s2016 gw | s |||| 0|eng d
020			_a9783319290751 _9978-3-319-29075-1
024	7		_a10.1007/978-3-319-29075-1 _2doi
050		4	_aQA292
050		4	_aQA295
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
072		7	_aPBK _2thema
082	0	4	_a515.24 _223
100	1		_aLoday-Richaud, Michèle. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aDivergent Series, Summability and Resurgence II _h[electronic resource] : _bSimple and Multiple Summability / _cby Michèle Loday-Richaud.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2016.
300			_aXXIII, 272 p. 64 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x0075-8434 ; _v2154
505	0		_aAvant-propos -- Preface to the three volumes -- Introduction to this volume -- 1 Asymptotic Expansions in the Complex Domain -- 2 Sheaves and Čech cohomology -- 3 Linear Ordinary Differential Equations -- 4 Irregularity and Gevrey Index Theorems -- 5 Four Equivalent Approaches to k-Summability -- 6 Tangent-to-Identity Diffeomorphisms -- 7 Six Equivalent Approaches to Multisummability -- Exercises -- Solutions to Exercises -- Index -- Glossary of Notations -- References.
520			_aAddressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second of a series of three entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes it can be read independently.
650		0	_aSequences (Mathematics).
650		0	_aDifferential Equations.
650		0	_aFunctional equations.
650		0	_aDifferentiable dynamical systems.
650	1	4	_aSequences, Series, Summability. _0http://scigraph.springernature.com/things/product-market-codes/M1218X
650	2	4	_aOrdinary Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12147
650	2	4	_aDifference and Functional Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12031
650	2	4	_aDynamical Systems and Ergodic Theory. _0http://scigraph.springernature.com/things/product-market-codes/M1204X
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319290744
776	0	8	_iPrinted edition: _z9783319290768
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v2154
856	4	0	_uhttps://doi.org/10.1007/978-3-319-29075-1
912			_aZDB-2-SMA
912			_aZDB-2-LNM
999			_c11192 _d11192