TY - JOUR AU - Zolotarev, V.A. PY - 2007/05/10 Y2 - 2024/03/29 TI - Scattering Scheme with Many Parameters and Translational Models of Commutative Operator Systems JF - Журнал математичної фізики, аналізу, геометрії JA - Журн. мат. фіз. анал. геом. VL - 3 IS - 4 SE - Статті DO - UR - http://jmag.ilt.kharkov.ua/index.php/jmag/article/view/jm03-0424e SP - 424-447 AB - The scattering scheme with many parameters for a commutative systemof linear bounded operators {<i>T</i><sub>1</sub>, <i>T</i><sub>2</sub>}, when <i>T</i><sub>1</sub> is a contraction, is built. Using this construction of the scattering scheme, the translation model ofthe semigroup with two parameters <i>T</i>(<i>n</i>) = <i>T<sub>1</sub><sup>n</i>1</sup> <i>T<sub>2</sub><sup>n</i>2</sup> , <i>n</i> = (<i>n</i><sub>1</sub>, <i>n</i><sub>2</sub>) <font face=`Symbol`>&Icirc;</font> Z<sub>+</sub><sup>2</sup> is obtained. Description of characteristic properties of the dilation <i>U</i> of the contraction <i>T</i><sub>1</sub>, that follows from the commutative property of the operators<i>T</i><sub>1</sub> and <i>T</i><sub>2</sub>, in terms of external parameters lies in the basis of the method of the construction of the translational models for <i>T</i>(<i>n</i>).<br><p><b>Mathematics Subject Classification: </b>47A45. ER -