Open Problems and Avenues for Further Research

The work we have done so far and which we have described in the last five chapters shows the power of algebraic analysis as well as the importance of the accessibility of suitable computational techniques. We have demonstrated how these ideas can greatly contribute to the development of a function theory for solutions of suitable systems of differential operators. However, many delicate questions remain open. In this short chapter we will analyze several lines of research which are strictly connected with the positive results obtained so far.