LEADER 03136nmm a2200409 i 4500 001 991003409299707536 007 cr cn ---mpcbr 008 170809s2016 sz | o j |||| 0|eng d 020 $a9783319290751 024 7 $a10.1007/978-3-319-29075-1$2doi 035 $ab14329359-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.24$223 084 $aAMS 40-02 100 1 $aLoday-Richaud, Michèle$0730102 245 10$aDivergent Series, summability and resurgence II$h[e-book] :$bSimple and multiple summability /$cby Michèle Loday-Richaud 264 1$aCham :$bSpringer,$c2016 300 $a1 online resource 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 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 ?ech 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 $aAddressing the question how to ?sum? a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya?s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second of a series of three entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes it can be read independently 650 0$aDifference equations 650 0$aFunctional equations 650 0$aDynamics 650 0$aErgodic theory 650 0$aDifferential equations 773 0 $aSpringer eBooks 776 08$iPrinted edition:$z9783319290744 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-29075-1$zAn electronic book accessible through the World Wide Web 907 $a.b14329359$b03-03-22$c09-08-17 912 $a991003409299707536 996 $aDivergent Series, Summability and Resurgence II$91474446 997 $aUNISALENTO 998 $ale013$b09-08-17$cm$d@ $e-$feng$gsz $h0$i0