Galois Theory of Difference Equations

Marius van der Put, Michael F. Singer (auth.)9783540632436, 3540632433

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.

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Table of contents :
Picard-Vessiot rings….Pages 4-27
Algorithms for difference equations….Pages 28-34
The inverse problem for difference equations….Pages 35-44
The ring S of sequences….Pages 45-51
An excursion in positive characteristic….Pages 52-59
Difference modules over $$mathcal{P}$$ ….Pages 60-67
Classification and canonical forms….Pages 71-76
Semi-regular difference equations….Pages 77-94
Mild difference equations….Pages 95-110
Examples of equations and galois groups….Pages 111-126
Wild difference equations….Pages 127-148
q -difference equations….Pages 149-174