Symbol functions for symmetric frameworks

We prove a variant of the well-known result that intertwiners for the bilateral shift on l(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. (C) 2020 The Authors. Published by Elsevier Inc.

Automated summary

In this paper, we prove a variant of the well-known result that intertwiners for the bilateral shift on l(2)(Z) are unitarily equivalent to multiplication operators on L-2(T). This allows us to unify and extend fundamental aspects of rigidity theory for bar-joint frameworks with an abelian symmetry group. Specifically, we formulate the symbol function for a wide class of frameworks and demonstrate how to construct generalised rigid unit modes in various new contexts.