VARIATIONS ON THE FUNDAMENTAL PRINCIPLE FOR LINEAR-SYSTEMS OF PARTIAL-DIFFERENTIAL AND DIFFERENCE-EQUATIONS WITH CONSTANT-COEFFICIENTS

New and known spaces of locally finite or polynomial exponential multivariate sequences and functions are constructed by means of substantial theorems from Commutative Algebra. They satisfy Ehrenpreis' fundamental principle and hence permit the solution of linear systems of partial differential or difference equations with constant coefficients. On the one hand this paper thus continues the author's work on multidimensional linear systems, on the other hand it generalizes and improves related work in approximation theory.