Abstract
The minimal numberμ(S) of generators of a multidimensional systemS is constructively determined. Such anS is the solution space of a linear system of partial differential or difference equations with constant coefficients. The main theorem generalizes recent results of Heij and Zampieri who calculated the numberμ(S) in the one- (resp. two-) dimensional discrete case. There is also a direct connection with Macaulay's inverse systems in the multidimensional discrete situation, in particular with his principal systems characterized by the relationμ(S)⩽1. It is surprising that, for dimensions greater than one, very many “large” systems are principal in this sense.
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Oberst, U. On the minimal number of trajectories determining a multidimensional system. Math. Control Signal Systems 6, 264–288 (1993). https://doi.org/10.1007/BF01211623
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DOI: https://doi.org/10.1007/BF01211623