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Symbol functions for symmetric frameworks

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Article number124895
<mark>Journal publication date</mark>15/05/2021
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number2
Number of pages24
Publication StatusPublished
Early online date8/01/21
<mark>Original language</mark>English


We prove a variant of the well-known result that intertwiners for the bilateral shift on l²(Z) are unitarily equivalent to multiplication operators on L²(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.