Concrete interpolation of meromorphic matrix functions on Riemann surfaces

This work investigates concrete problems of interpolating matrix pole-zero data with multiple-valued meromorphic matrix functions on closed Riemann surfaces. In the case of genus g > 1, a condition sufficient for the existence of a solution having constant factor of automorphy is presented. Necessary and sufficient conditions are presented in the case where g = 1. A necessary and sufficient condition for single-valued matrix function interpolation in arbitrary genus is also established.