A SOLUTION OF THE CAUCHY-PROBLEM FOR MULTIDIMENSIONAL DISCRETE LINEAR SHIFT-INVARIANT SYSTEMS

We propose a solution of the Cauchy problem for multidimensional linear shift-invariant systems over Z(r) that can be described by a set of multidimensional difference equations. We give a method for finding an initial condition structure. it consists in finding subsets of Z(r) where the signals can be given arbitrarily and where they fix the trajectory on the whole grid. Moreover we develop an efficient algorithm computing the whole trajectory, once given the initial conditions. For this purpose we develop some constructive techniques for Laurent polynomial modules.