We shall consider the following generalized NEHARI problem (N): Let a : D + A p x p , 8 : D + A, be matrix functions which are holomorphic in ED. Give necessary and sufficient Conditions for the existence of a matrix function g: D + Jtqxp such that and d : Pp + A,
belongs to gp+q. Describe the set of all matrix functions
We shall present necessary and sufficient conditions for the solvability of (N) in terms of the TAYLOR coefficients of u, /3 and 6. We shall obtain a choice sequence type parametrization of the set of all solutions of (N) by successive iteration of certain one-step extension procedures. I n other extension problems procedures of this kind were given e.g. by ADAMJAN/AROV/KREIN [4], DYM/GOHBERG [23], ARSENE/CEAUSE~CU/ FOIAS [17], CONSTANTINESCU [19], [20] and by the authors [25], [26]. Th;? problem (N) is a generalization of a classical problem due to NEELARI 1341. Fundamental results connected t.0 this classical problem were obtained by ADABIJAN, AROV and KREIN in their famous papers [l], [2], [3], [4]. I n particular, they also discussed the matricial version of the original NEHARI problem (compare [4]). Later we shall indicate that this matricial NEHARI problem is a special case of the above problem (N)-for which 3 E gp+q.