Rational contractive and unitary interpolants in realized form
The Nehari (interpolation) problem is to find for a given sequence L of matrices all corresponding matrix functions f satisfying two certain conditions. A great contribution is done by \textit{V. M. Adamjan}, \textit{D. Z. Arov} and \textit{M. G. Krejn} [see, for instance, Funkts. Anal. Prilozb. 2, No.4, 1-12 (1968; Zbl 0179.467)]. The present authors take a new approach standing on \textit{H. Dym} and \textit{I. Gohberg} [J. Funct. Anal., 54, 229-289 (1983; Zbl 0534.47009) and 65, 83-125 (1986; Zbl 0588.47020)], and in particular give a solution for rational f on the unit circle in terms of a realization (A,B,C), which is a certain triple of matrices associated with L. For further information (on the problem), refer to \textit{J. B. Garnett} [Bounded Analytic Functions (1981; Zbl 0469.30024)], \textit{S. C. Power} [Hankel Operators on Hilbert Space (1982; Zbl 0489.47011)], \textit{B. A. Francis} and \textit{J. Doyle} [Systems Control Group Report, No.8501, Univ. of Toronto (1985)], \textit{C. Foias} and \textit{A. Tannenbaum} [J. Funct. Anal. 74, 146-159 (1987; Zbl 0635.47027)], etc.
scientific article; zbMATH DE number 4060153
scientific article