On Bitangential Interpolation in the Time Varying Setting for Hilbert-Schmidt Operators: The Continuous Case
The Hilbert space of lower triangular Hilbert–Schmidt operators on the real line is a natural analogue of the Hardy space of a half-plane, where the complex numbers are now replaced by matrix-valued functions. One can associate with a bounded operator its “values” at a matrix-valued function [see Ballet al.,Oper. Theory Adv. Appl.56(1992), 52–89], and this allows [see Ballet al.,Integral Equations Operator Theory20(1994), 1–43] to define and solve the analogue of the two-sided Nudelman interpolation problem for bounded operators (which form an analogue ofH∞(C+)). In this paper we consider the two-sided interpolation problem with a Hilbert–schmidt norm constraint (rather than the more common operator-norm constraint) on the interpolant.
D. Alpay, V. Bolotnikov, B. Freydin and Y. Peretz. On bitangential interpolation in the time varying setting for Hilbert-Schmidt operators: the continuous case. Journal of Mathematical Analysis and Applications, vol. 228 (1998) pp. 275-292.