The constructive solution of linear systems of partial difference and differential equations with constant coefficients

This paper gives a survey of past work in the treated subject and also cont ains several new results. We solve the Cauchy problem for linear systems of partial difference equations on general integral lattices by means of suit able transfer operators and show that these can be easily computed with the help of standard implementations of Grobner basis algorithms. The Borel is omorphism permits to transfer these results to systems of partial different ial equations. We also solve the Cauchy problem for the function spaces of convergent power series and for entire functions of exponential type. The u nique solvability of the Cauchy problem implies that the considered functio n spaces are large injective cogenerators for which the duality between fin itely generated modules and behaviours holds. Already in the beginning of t he last century C. Riquier considered and solved problems of the type discu ssed here.