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Divergent series, summability and re...

Loday-Richaud, Michele.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Divergent series, summability and resurgence./ by Michele Loday-Richaud.
其他題名:	Simple and multiple summability
作者:	Loday-Richaud, Michele.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xxiii, 272 p. :ill., digital ;24 cm.
內容註:	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
標題:	Divergent series. -
電子資源:	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

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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.
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