.
We introduce a class of matrix-valued functions W called “L 2- regular”. In case W is J-inner, this class coincides with the class of “strongly regular J-inner” matrix functions in the sense of Arov–Dym. We show that the class of L 2-regular matrix functions is exactly the class of transfer functions for a discrete-time dichotomous (possibly infinite-dimensional) input-state-output linear system having some additional stability properties. When applied to J-inner matrix functions, we obtain a state-space realization formula for the resolvent matrix associated with a generalized Schur–Nevanlinna–Pick interpolation problem.
Communicated by Daniel Alpay