On an interpolation problem for J-Potapov functions

The main goal of this paper is the study of an analogue of the matricial Schur problem for the Potapov class PJ(D) of J-contractive meromorphic functions in the open unit disk D. Using an approach which is based on an analysis of J-central J-Potapov functions, we will solve this problem in the most general case. Moreover, in the nondegenerate case we will give a description of the corresponding Weyl matrix balls. Furthermore, we will investigate the limit behaviour of the Weyl matrix balls associated with the functions belonging to some particular subclass of PJ(D).