On block completion problems for Arov-normalized \(j_{qq}-J_{q}\)-elementary factors
It is well known that the matrix completion problems are equivalent to interpolation problems for classes of analytic functions. It was also understood very early in the development of this dictionary that considering indefinite metric spaces can simplify and illuminate classical computations first considered by Schur, Carathéodory and Nevanlinna and can be used in Hamiltonian mechanics problems. The present note is a part of an ample programme advocated by the first two authors. Specifically, the note deals with a non-degenerate Carathéodory interpolation problem, for matrix valued analytic functions, which are contractive (respectively unitary on the boundary) with respect to a \(J\)-inner product structure. The work is based on old ideas of Potapov and their more recent ramifications due to Arov. See for instance: \textit{D. Z. Arov} [Teor. Funkts. Funkts. Anal. Priloz. 51, 61-67 (1989; Zbl 0701.41006); ibid. 52, 103-109 (1989; Zbl 0737.41001); ibid. 53, 57-65 (1990; Zbl 0738.47015)].
non-degenerate Carathéodory interpolation problem
scientific article; zbMATH DE number 1758618