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Galois Theory of Difference Equations

  • Book
  • © 1997

Overview

Authors:
  1. Marius Put
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  2. Michael F. Singer
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1666)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-VII
    Download chapter PDF

  2. Picard-Vessiot rings

    • Marius van der Put, Michael F. Singer
    Pages 4-27

  3. Algorithms for difference equations

    • Marius van der Put, Michael F. Singer
    Pages 28-34

  4. The inverse problem for difference equations

    • Marius van der Put, Michael F. Singer
    Pages 35-44

  5. The ring S of sequences

    • Marius van der Put, Michael F. Singer
    Pages 45-51

  6. An excursion in positive characteristic

    • Marius van der Put, Michael F. Singer
    Pages 52-59

  7. Difference modules over \(\mathcal{P}\)

    • Marius van der Put, Michael F. Singer
    Pages 60-67

  8. Classification and canonical forms

    • Marius van der Put, Michael F. Singer
    Pages 71-76

  9. Semi-regular difference equations

    • Marius van der Put, Michael F. Singer
    Pages 77-94

  10. Mild difference equations

    • Marius van der Put, Michael F. Singer
    Pages 95-110

  11. Examples of equations and galois groups

    • Marius van der Put, Michael F. Singer
    Pages 111-126

  12. Wild difference equations

    • Marius van der Put, Michael F. Singer
    Pages 127-148

  13. q-difference equations

    • Marius van der Put, Michael F. Singer
    Pages 149-174

  14. Back Matter

    Pages 175-180
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Keywords

About this book

This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

Bibliographic Information

  • Book Title: Galois Theory of Difference Equations

  • Authors: Marius Put, Michael F. Singer

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096118

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63243-6Published: 18 September 1997

  • eBook ISBN: 978-3-540-69241-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 188

  • Topics: Analysis, Algebra

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