Interpolation and approximation of quasiseparable systems: The Schur-Takagi case

We explore how the classical Schur-Takagi interpolation theory as developed by Chamfy, Krein and Langer and Alpay, Azizov, Dijksma, and Langer generalizes to the matrix/operator case in the context of quasiseparable representations. A surprising result is that the generic case in the classical theory is no longer generic for the matrix case; it becomes a rather rare special case. This confirms again the general statement that the non-stationary case is essentially different from the index- or time-invariant case in contrast to common opinion.