论文标题
berger-coburn-lebow表示产品系统的纯等距表示，$ \ mathbb n^2_0 $
Berger-Coburn-Lebow representation for pure isometric representations of product system over $\mathbb N^2_0$
论文作者
论文摘要
我们获得了Berger-Coburn-Lebow（BCL） - 在$ \ Mathbb {n} _0^2 $上的纯等距协变代表代表。然后研究了相应的（关节）统一不变的集合，并将BCL表示与纯等距协变量表示的其他规范多分析描述进行了比较。我们表征了纯等距协变量表示的不变子空间。此外，我们研究了联合缺陷操作员和边缘操作员之间的联系，在这种情况下，介绍了弗雷德姆指数。最后，我们介绍了一致性关系的概念，以通过$ \ mathbb {n} _0^2 $对产品系统的等值变量表示进行分类。
We obtain Berger-Coburn-Lebow (BCL)-representation for pure isometric covariant representation of product system over $\mathbb{N}_0^2$. Then the corresponding complete set of (joint) unitary invariants is studied, and the BCL- representations are compared with other canonical multi-analytic descriptions of the pure isometric covariant representation. We characterize the invariant subspaces for the pure isometric covariant representation. Also, we study the connection between the joint defect operators and Fringe operators, and the Fredholm index is introduced in this case. Finally, we introduce the notion of congruence relation to classify the isometric covariant representations of the product system over $\mathbb{N}_0^2$.
