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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.

Group theory --- Functional analysis --- Difference equations --- Galois theory --- Mathematical Theory --- Operations Research --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Equations aux differences --- Galois [Theorie de ] --- Galois [Theorie van ] --- Vergelijkingen met differenties --- Mathematical analysis. --- Analysis (Mathematics). --- Algebra. --- Analysis. --- Mathematical analysis --- 517.1 Mathematical analysis --- Difference equations. --- Galois theory. --- Equations, Theory of --- Number theory --- Calculus of differences --- Differences, Calculus of --- Equations, Difference

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Number theory --- Algebraic fields --- Algebraic numbers --- Algebraïsche velden --- Corps algébriques --- Fields [Algebraic ] --- Galois [Theorie de ] --- Galois [Theorie van ] --- Galois theory --- Homologie --- Homology theory --- Théorie de Galois --- Algebraic fields. --- Galois theory. --- Homology theory. --- Corps algébriques --- Théorie de Galois --- Nombres, Théorie des. --- Number theory. --- Cohomologie. --- Galois cohomology --- Cohomologie galoisienne. --- Nombres, Théories des --- Cohomologie --- Cohomologie galoisienne --- Nombres, Théorie des --- Nombres algébriques, Théorie des