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

作者： Werner Balser著

出 版 社：

出版时间： 1999-10-1字数：版次： 1页数： 299印刷时间： 1999/10/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387986906包装： 精装内容简介

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.

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