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.
General
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