Galois Theory of Difference Equations

1997
ISBN: 978-3-540-63243-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1666, 188 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 306 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Singer, Michael F.

Put, Marius van der

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.