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001 | 978-3-319-29075-1 | ||
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008 | 160628s2016 gw | s |||| 0|eng d | ||
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_a9783319290751 _9978-3-319-29075-1 |
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_a10.1007/978-3-319-29075-1 _2doi |
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_a515.24 _223 |
100 | 1 |
_aLoday-Richaud, Michèle. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aXXIII, 272 p. 64 illus. in color. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2154 |
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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 | |
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_iPrinted edition: _z9783319290744 |
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_iPrinted edition: _z9783319290768 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2154 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-29075-1 |
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