Accepted author manuscript, 465 KB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Symbol functions for symmetric frameworks
AU - Kastis, Eleftherios
AU - Kitson, Derek
AU - McCarthy, John
PY - 2021/5/15
Y1 - 2021/5/15
N2 - 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.
AB - 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.
U2 - 10.1016/j.jmaa.2020.124895
DO - 10.1016/j.jmaa.2020.124895
M3 - Journal article
VL - 497
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
M1 - 124895
ER -