SUMMARY OF RECENT RESULTS ON THE SCALAR RATIONAL INTERPOLATION PROBLEM.

A summary of the results obtained by the author in a 1986 publication is presented. The main result asserts that the minimal degree of the interpolating function(s) is either rank L or N-rank L, according to whether certain explicitly stated conditions are satisfied or not. In the former case the minimal interpolating function is unique, while in the latter it is non-unique, having N-2rank L plus 1 degrees of freedom. A parametrization of all minimal and non-minimal interpolating functions follows. The problems of proper rational and polynomial interpolation are briefly examined.