ON THE MINIMAL NUMBER OF TRAJECTORIES DETERMINING A MULTIDIMENSIONAL SYSTEM

The minimal number mu(S) of generators of a multidimensional system S is constructively determined. Such an S is the solution space of a lin ear system of partial differential or difference equations with consta nt coefficients. The main theorem generalizes recent results of Heij a nd Zampieri who calculated the number mu(S) in the one- (resp. two-) d imensional discrete case. There is also a direct connection with Macau lay's inverse systems in the multidimensional discrete situation, in p articular with his principal systems characterized by the relation mu( S) less-than-or-equal-to 1. It is surprising that, for dimensions grea ter than one, very many ''large'' systems are principal in this sense.