Integral triangular operators and Friedrichs model

In the present paper we investigate a semi-group of triangular integral operators $V_{\beta }$, which is an analogue of the semi-group of the fractional integral operators $J^{\beta }$. With the help of these semi-groups, we construct and study two classes of triangular Friedrichs models $A_{\beta }$ and $B_{\beta }$, respectively. Using generalized wave operators we prove that $A_{\beta }$ and $B_{\beta }$ are linearly similar to a self-adjoint operator with absolutely continuous spectrum.