Paper detail

Integral triangular operators and Friedrichs model

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