Notes on Difference Equations
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چکیده
We shall develop here a galois theory for difference equations. In the PicardVessiot galois theory for differential equations, the basic objects of study are the Picard-Vessiot extension of a field and its associated galois group. Recall that a Picard-Vessiot extension of a differential field k is an extension K generated by a fundamental set of solutions of a linear differential equation and having the same field of constants as k. The automorphism group of K over k is an algebraic group and, if the field of constants is algebraically closed, the fixed field of this group is k. When one tries to mimic this approach for difference equations one is confronted with the following example:
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