Galois Theory of Difference Equations / Edition 1

by Marius van der Put, Michael F. Singer

Overview

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.

Product Details

ISBN-13:	9783540632436
Publisher:	Springer Berlin Heidelberg
Publication date:	10/29/1997
Series:	Lecture Notes in Mathematics , #1666
Edition description:	1997
Pages:	188
Product dimensions:	10.00(w) x 11.40(h) x 1.30(d)

Table of Contents

Picard-Vessiot rings.- Algorithms for difference equations.- The inverse problem for difference equations.- The ring S of sequences.- An excursion in positive characteristic.- Difference modules over .- Classification and canonical forms.- Semi-regular difference equations.- Mild difference equations.- Examples of equations and galois groups.- Wild difference equations.- q-difference equations.