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Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations

  • Textbook
  • © 2000

Overview

Authors:
  1. Werner Balser

    1. Abteilung Mathematik V, Universität Ulm, Ulm, Germany

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Part of the book series: Universitext (UTX)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Basic Properties of Solutions

    Pages 1-16

  3. Singularities of First Kind

    Pages 17-36

  4. Highest-Level Formal Solutions

    Pages 37-58

  5. Asymptotic Power Series

    Pages 59-76

  6. Integral Operators

    Pages 77-96

  7. Summable Power Series

    Pages 97-114

  8. Cauchy-Heine Transform

    Pages 115-122

  9. Solutions of Highest Level

    Pages 123-138

  10. Stokes’ Phenomenon

    Pages 139-158

  11. Multisummable Power Series

    Pages 159-174

  12. Ecalle’s Acceleration Operators

    Pages 175-182

  13. Other Related Questions

    Pages 183-196

  14. Applications in Other Areas, and Computer Algebra

    Pages 197-205

  15. Some Historical Remarks

    Pages 207-210

  16. Back Matter

    Pages 211-299
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Keywords

About this book

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.

Authors and Affiliations

  • Abteilung Mathematik V, Universität Ulm, Ulm, Germany

    Werner Balser

Bibliographic Information

  • Book Title: Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations

  • Authors: Werner Balser

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/b97608

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • Hardcover ISBN: 978-0-387-98690-6Published: 29 October 1999

  • Softcover ISBN: 978-1-4757-7405-4Published: 01 May 2013

  • eBook ISBN: 978-0-387-22598-2Published: 19 January 2008

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XVIII, 301

  • Topics: Analysis

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