Multiparametric dissipative linear stationary dynamical scattering systems: Discrete case. II: Existence of conservative dilations
The author studies multiparameter linear stationary dynamical systems (LSDSs). Such systems represent a generalization of LSDSs with discrete time \(t\in \mathbb Z\), in particular dissipative (contractive), and conservative (unitary) scattering systems, to the case \(t\in \mathbb Z^n\). The notion of a dilation of a multiparameter LSDS is introduced, and a criterion is given for existence of a conservative dilation of a dissipative system. The class of transfer functions of all dissipative scattering LSDSs (with given input and output spaces) possessing conservative dilations is characterized. It is a subclass of the generalized Schur class of operator-valued functions on the open unit polydisk.
multiparameter linear stationary dynamical systems
scientific article; zbMATH DE number 1417546