One approach to the problem of partial realization

The paper is concerned with an approach to the problem of partial realization of multi-dimensional linear stationary discrete-time systems. Using this approach, the problem of extended partial realization in.the scalar case is formulated and solved. The solution is found to be related with algebraical problems; the difficulties in solving a multi-dimensional problem of partial realization are shown to be caused by the difficulties in extending the above algebraical problems to the multi-dimensional case.