On J-conservative scattering system realization in several variables

Abstract

We prove that an arbitrary function, which is holomorphic on some neighbourhood of z=0 in $\mathbb{C}^N$ and vanishes at z=0, whose values are bounded linear operators mapping one separable Hilbert space into another one, can be represented as the transfer function of some multiparametric discrete time-invariant conservative scattering linear system with a Krein space of its inner states.