INNER OUTER FACTORIZATION OF NONLINEAR OPERATORS

A fundamental result in the theory of Hardy spaces of analytic matrix and operator valued functions on the unit disk is inner-outer factorization. For the case of rational matrix functions, explicit formulas for the inner and outer factors have recently been obtained; in these formulas the functions are presented in terms of a collection of finite matrices as the transfer function of a linear system. The key ingredient in the construction is the solution of a linear matrix equation (called a Stein equation). In this paper we obtain extensions of these results to the setting of input-output maps of nonlinear discrete-time systems. A particaular computable class of examples is presented for illustration. © 1992.