On Bitangential Interpolation in the Time-Varying Setting for Hilbert]Schmidt Operators: The Continuous Time 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 wsee Ball et al., Oper. Theory Ad¨. Appl. 56 1992., 52]89x, and this allowswsee Ball et al., Integral Equations Operator Theory 20 1994., 1]43x to define and solve the analogue of the two-sided Nudelman interpolation problem for bounded operators which form an analogue of H C ... In this paper we consider the two-sided interpolation ` q problem with a Hilbert]schmidt norm constraint rather than the more common operator-norm constraint. on the interpolant