积分三角算子与Friedrichs模型
Integral triangular operators and Friedrichs model
摘要：
本文研究了三角积分算子半群$V_β$，它是分数次积分算子半群$J^β$的一个类似.借助于这些半群，我们分别构造和研究了两类三角Friedrichs模型$A_β$和$B_β$.利用广义波算子证明了$A_β$和$B_β$线性相似于具有绝对连续谱的自伴算子.
英文摘要：
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.
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