Scattering Scheme with Many Parameters and Translational Models of Commutative Operator Systems

Abstract

The scattering scheme with many parameters for a commutative system of linear bounded operators {T1; T2}, when T1 is a contraction, is built. Using this construction of the scattering scheme, the translation model of the semigroup with two parameters T(n) = T1^n1 T2^n2 , n = (n1; n2) belongs Z+^2 is obtained. Description of characteristic properties of the dilation U of the contraction T1, that follows from the commutative property of the operators T1 and T2, in terms of external parameters lies in the basis of the method of the construction of the translational models for T(n).