LEADER 04282nam 22006975 450 001 9910137016903321 005 20200705014202.0 010 $a3-319-29075-4 024 7 $a10.1007/978-3-319-29075-1 035 $a(CKB)3710000000734917 035 $a(DE-He213)978-3-319-29075-1 035 $a(MiAaPQ)EBC6285133 035 $a(MiAaPQ)EBC5587993 035 $a(Au-PeEL)EBL5587993 035 $a(OCoLC)953243796 035 $a(PPN)194378233 035 $a(EXLCZ)993710000000734917 100 $a20160628d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDivergent Series, Summability and Resurgence II $eSimple and Multiple Summability /$fby Michèle Loday-Richaud 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XXIII, 272 p. 64 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2154 311 $a3-319-29074-6 327 $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. 330 $aAddressing the question how to ?sum? a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya?s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second of a series of three entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes it can be read independently. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2154 606 $aSequences (Mathematics) 606 $aDifferential equations 606 $aDifference equations 606 $aFunctional equations 606 $aDynamics 606 $aErgodic theory 606 $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 615 0$aSequences (Mathematics). 615 0$aDifferential equations. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aDynamics. 615 0$aErgodic theory. 615 14$aSequences, Series, Summability. 615 24$aOrdinary Differential Equations. 615 24$aDifference and Functional Equations. 615 24$aDynamical Systems and Ergodic Theory. 676 $a510 700 $aLoday-Richaud$b Michèle$4aut$4http://id.loc.gov/vocabulary/relators/aut$0730102 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910137016903321 996 $aDivergent Series, Summability and Resurgence II$91474446 997 $aUNINA