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): 124895. ISSN 0022-247X

Text (Symbol functions for symmetric frameworks Kastis Kitson McCarthy)
Symbol_functions_for_symmetric_frameworks_Kastis_Kitson_McCarthy.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (476kB)

Abstract

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.