國立虎尾科技大學 |

Divergent series, summability and resurgence.. II,. Simple and multiple summability

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Divergent series, summability and resurgence./ by Michele Loday-Richaud.
remainder title:	Simple and multiple summability
Author:	Loday-Richaud, Michele.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xxiii, 272 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Divergent series. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-29075-1
ISBN:	9783319290751

Divergent series, summability and resurgence.. II,. Simple and multiple summability
Loday-Richaud, Michele.

Divergent series, summability and resurgence.II,Simple and multiple summability[electronic resource] /Simple and multiple summabilityby Michele Loday-Richaud. - Cham :Springer International Publishing :2016. - xxiii, 272 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21540075-8434 ;. - Lecture notes in mathematics ;1943..

Avant-propos -- Preface to the three volumes -- Introduction to this volume -- 1 Asymptotic Expansions in the Complex Domain -- 2 Sheaves and Cech 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.

Addressing 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.

ISBN: 9783319290751

Standard No.: 10.1007/978-3-319-29075-1doiSubjects--Topical Terms:

1110680
Divergent series.

LC Class. No.: QA295

Dewey Class. No.: 515.243

Divergent series, summability and resurgence.. II,. Simple and multiple summability
LDR:02752nam a2200337 a 4500 001 865263
003 DE-He213
005 20161129112304.0
006 m d
007 cr nn 008maaau
008 170720s2016 gw s 0 eng d
020 $a 9783319290751 $q (electronic bk.)
020 $a 9783319290744 $q (paper)
024 7 $a 10.1007/978-3-319-29075-1 $2 doi
035 $a 978-3-319-29075-1
040 $a GP $c GP
041 1 $a eng $b fre $h eng
050 4 $a QA295
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.243 $2 23
090 $a QA295 $b .L821 2016
100 1 $a Loday-Richaud, Michele. $3 1110681
245 1 0 $a Divergent series, summability and resurgence. $n II, $p Simple and multiple summability $h [electronic resource] / $c by Michele Loday-Richaud.
246 3 0 $a Simple and multiple summability
260 $a Cham : $c 2016. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxiii, 272 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2154
505 0 $a Avant-propos -- Preface to the three volumes -- Introduction to this volume -- 1 Asymptotic Expansions in the Complex Domain -- 2 Sheaves and Cech 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 $a Addressing 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 $a Divergent series. $3 1110680
650 0 $a Summability theory. $3 867471
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Sequences, Series, Summability. $3 672022
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Difference and Functional Equations. $3 672077
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 1943. $3 882220
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-29075-1
950 $a Mathematics and Statistics (Springer-11649)