The constructive solution of the cauchy problem for linear systems of partial difference or differential equations with constant coefficients

In this talk we solve the problem of the title. Compared to earlier work we give a fast and direct algorithm for the computation of the transfer operators of the discrete Cauchy problem over general submonoids of Z^r instead of N^r and also consider the case of convergent solutions. For the latter situation we use ideas of C. Riquier [1910!].