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 {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) = T₁ⁿ1 T₂ⁿ2 , n = (n₁, n₂) Î 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).

Mathematics Subject Classification: 47A45.