Symbol functions for symmetric frameworks

Kastis, Eleftherios and Kitson, Derek and McCarthy, John (2021) Symbol functions for symmetric frameworks. Journal of Mathematical Analysis and Applications, 497 (2). ISSN 0022-247X

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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.

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Journal Article
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Journal of Mathematical Analysis and Applications
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Deposited On:
04 Jan 2021 11:45
Last Modified:
17 Sep 2023 02:57