Multiparametric dissipative linear stationary dynamical scattering systems: discrete case

摘要

We propose the new generalization of linear stationary dynamical systems with discrete time t ∈ Z to the case t ∈ Z~N. The dynamics of such a system can be reproduced by means of its associated multiparametric Lax-Phillips semigroup. We define multiparametric dissipative and conservative scattering systems and interpret them in terms of operator colligations, of the associated semigroup, and of "energy" relations for system data. We prove the Agler's type theorem describing the class of holomorphic operator-valued functions on the polydisc D~N that are the transfer functions of multiparametric conservative scattering systems.