On the universal models of commutative systems of linear operators

The universal models are constructed for a system of linear bounded non-selfadjoint operators $\{A_1,A_2\}$ acting in a Hilbert space $H$ such that 1) $[A_1,A_2]=0$, $[A_1^*,A_2]=0$; 2) $\displaystyle{\frac{A_k-A_k^*}i\geq0}$ ($k=1, 2$); 3) the function $A(\lambda)=A_1(\lambda_1)A_2(\lambda_2)$ ($A_k(\lambda_k)=A_k(I-\lambda_kA_k)^{-1}$, $k=1, 2$) is an entire function of the exponential type. It is proved that this class of linear operator systems is realized by the restriction on invariant subspaces of systems of operator of integration by independent variables in $L^2(\Omega)\otimes l^2$ where $\Omega$ is a rectangle in $\mathbb{R}^2$.