论文标题
对称框架的符号功能
Symbol functions for symmetric frameworks
论文作者
论文摘要
我们证明了众所周知的结果的一种变体，即双边偏移的互穿$ \ ell^2（z）$在$ l^2（t）$上的乘法运算符上等同于单位。这使我们能够通过阿贝尔对称群体统一和扩展僵化理论的基本方面。特别是，我们为各种框架制定了符号函数，并展示了如何在各种新上下文中构建通用的刚性单元模式。
We prove a variant of the well-known result that intertwiners for the bilateral shift on `$\ell^2(Z)$ are unitarily equivalent to multiplication operators on $L^2(T)$. This enables us to unify and extend fundamental aspects of rigidity theory for bar-joint frameworks with an abelian symmetry group. In particular, we formulate the symbol function for a wide class of frameworks and show how to construct generalised rigid unit modes in a variety of new contexts.
