On \(J\)-conservative scattering system realizations in several variables. (Q1865935)

The author presents a multivariable generalization of the result about the \(J\)-conservative scattering system realization for an operator-valued function holomorphic in a neighborhood of zero, due to \textit{T. Ya. Azizov} and \textit{I. S. Iokhvidov} [``Linear operators in space with an indefinite metric'' (Pure and Applied Mathematics, John Wiley \& Sons, Chichester) (1989; Zbl 0714.47028)]. In order to obtain the main existence result, he introduces notion of multi-parameter discrete time-invariant \(J\)-conservative scattering linear system, proves that an arbitrary multi-parameter linear system has a \(J\)-conservative scattering system dilation, and uses the fact that the transfer function of a multi-parameter linear system remains the same under dilation.