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Formal power series and linear systems of meromorphic ordinary differential equations亚纯常微分方程的形式幂级数与线性系统

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Formal power series and linear systems of meromorphic ordinary differential equations亚纯常微分方程的形式幂级数与线性系统

最 低 价:¥512.20

定 价:¥683.00

作 者:WernerBalser 著

出 版 社:

出版时间:1999-10-1

I S B N:9780387986906

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内容简介

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.

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目录

Preface
1 Basic Properties of Solutions
2 Singularities of First Kind
3 Highest-Level Formal Solutions
4 Asymptotic Power Series
5 Integral Operators
6 Summable Power Series
7 Cauchy-Heine Transform
8 Solutions of Highest Level
9 Stokes' Phenomenon
10 Multisummable Power Series
11 Ecalle's Acceleration Operators
12 Other Related Questions
13 Applications in Other Areas, and Computer Algebra
14 Some Historical Remarks
A Matrices and Vector Spaces
B Functions with Values in Banach Spaces
C Functions of a Matrix
Solutions to the Exercises
References
Index
List of Symbols

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