Difference equations in several variables
The result of Lefranc on spectral synthesis in F(ℤ n ) can be used to give a simple method for the solution of linear systems of homogeneous difference equations with constant coefficients. The method is based on the simple fact that varieties in F(ℤ n ) are exactly the solution spaces of such systems of equations. In the case n = 1 the situation reduces to the classical theory of linear homogeneous difference equations with constant coefficients, as it has been exhibited in Section 2.4. Now we present a more detailed analysis of this subject in several variables (see ). First we recall and adjust our previous notation to the present situation.
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