東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Divergent series, summability and re...

Loday-Richaud, Michele.

Linked to FindBook

Google Book

Amazon

博客來

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

Record Type:	Electronic resources : 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.
[NT 15003449]:	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.
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 ;2046..

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:

728335
Divergent series.

LC Class. No.: QA295

Dewey Class. No.: 515.243

Divergent series, summability and resurgence.. II,. Simple and multiple summability
LDR:02752nmm a2200337 a 4500 001 2041592
003 DE-He213
005 20161129112304.0
006 m d
007 cr nn 008maaau
008 170118s2016 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 2200309
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 : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
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 728335
650 0 $a Summability theory. $3 612604
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Sequences, Series, Summability. $3 897266
650 2 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Difference and Functional Equations. $3 897290
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 2046. $3 1534285
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-29075-1
950 $a Mathematics and Statistics (Springer-11649)