Tangential interpolation problems for a class of automorphic matrix-functions (Q1774967)

The authors consider an interpolation problem called the \((A,B,C)\)-problem (see \textit{A. A. Nudel'man} [Sov. Math., Dokl. 18, 507--510 (1977); translation from Dokl. Akad. Nauk SSSR 233, 792--795 (1977; Zbl 0372.30039); Oper. Theory, Adv. Appl. 61, 171--188 (1993; Zbl 0796.47007)] for details) in the class \((R)_\Gamma\), consisting of matrix-valued functions in Nevanlinna clas \((R)\) which are invariant under some fixed linear fractional transformation \(\Gamma\) of the upper half-plane into itself. They develop an abstract scheme of the problem and give a formula for the description of all invariant solutions of the abstract problem in the completely indeterminate case. They also show that the abstract scheme works for the case of the \((A,B,C)\)-problem, which generalizes the classical Nevanlinna--Pick problem.