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

Анотація

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 $T(n)=T_1^{n_1}T_2^{n_2}$ , $n=(n_1,n_2)\in {\mathbb Z}^2_{+}$ 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.