Scattering Scheme with Many Parameters and Translational Models of Commutative Operator Systems - Zolotarev, V. A. (Журнал математичної фізики, аналізу, геометрії, 2007)
The scattering scheme with many parameters for a commutative system of linear bounded operators {T_1,T_2}, when T_1 is a contraction, is built. Using this construction of the scattering scheme, the translation model of the semigroup with two parameters T(n)=T_1^n_1T_2^n_2 , n=(n_1,n_2)Z^2_+ is obtained. Description of characteristic properties of the dilation U of the contraction T_1, that follows from the commutative property of the operators T_1 and T_2, in terms of external parameters lies in the basis of the method of the construction of the translational models for T(n). Mathematics Subject Classification: 47A45.