Standard
Crystal frameworks, matrix-valued functions and rigidity operators. /
Power, Stephen.
Concrete operators, spectral theory, operators in harmonic analysis and approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011. ed. / Manuel Cepedello Boiso; Håkan Hedenmalm; Marinus A. Kaashoek; Alfonso Montes Rodríguez; Sergei Treil. Basel: Springer, 2014. p. 405-420 (Operator Theory: Advances and Applications; Vol. 236).
Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review
Harvard
Power, S 2014,
Crystal frameworks, matrix-valued functions and rigidity operators. in MC Boiso, H Hedenmalm, MA Kaashoek, AM Rodríguez & S Treil (eds),
Concrete operators, spectral theory, operators in harmonic analysis and approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011. Operator Theory: Advances and Applications, vol. 236, Springer, Basel, pp. 405-420.
https://doi.org/10.1007/978-3-0348-0648-0_26
APA
Power, S. (2014).
Crystal frameworks, matrix-valued functions and rigidity operators. In M. C. Boiso, H. Hedenmalm, M. A. Kaashoek, A. M. Rodríguez, & S. Treil (Eds.),
Concrete operators, spectral theory, operators in harmonic analysis and approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 (pp. 405-420). (Operator Theory: Advances and Applications; Vol. 236). Springer.
https://doi.org/10.1007/978-3-0348-0648-0_26
Vancouver
Power S.
Crystal frameworks, matrix-valued functions and rigidity operators. In Boiso MC, Hedenmalm H, Kaashoek MA, Rodríguez AM, Treil S, editors, Concrete operators, spectral theory, operators in harmonic analysis and approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011. Basel: Springer. 2014. p. 405-420. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0348-0648-0_26
Author
Power, Stephen. /
Crystal frameworks, matrix-valued functions and rigidity operators. Concrete operators, spectral theory, operators in harmonic analysis and approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011. editor / Manuel Cepedello Boiso ; Håkan Hedenmalm ; Marinus A. Kaashoek ; Alfonso Montes Rodríguez ; Sergei Treil. Basel : Springer, 2014. pp. 405-420 (Operator Theory: Advances and Applications).
Bibtex
@inproceedings{920316ec07de4f50b5e76b262a0911d9,
title = "Crystal frameworks, matrix-valued functions and rigidity operators",
abstract = "An introduction and survey is given of some recent work on the infinitesimal dynamics of crystal frameworks, that is, of translationally periodic discrete bond-node structures in ℝd, for d = 2,3,... We discuss the rigidity matrix, a fundamental object from finite bar-joint framework theory, rigidity operators, matrix-function representations and low energy phonons. These phonons in material crystals, such as quartz and zeolites, are known as rigid unit modes, or RUMs, and are associated with the relative motions of rigid units, such as SiO4 tetrahedra in the tetrahedral polyhedral bondnode model for quartz. We also introduce semi-infinite crystal frameworks, bi-crystal frameworks and associated multi-variable Toeplitz operators.",
keywords = "Rigidity operator",
author = "Stephen Power",
year = "2014",
doi = "10.1007/978-3-0348-0648-0_26",
language = "English",
isbn = "9783034806473",
series = "Operator Theory: Advances and Applications",
publisher = "Springer",
pages = "405--420",
editor = "Boiso, {Manuel Cepedello} and Hedenmalm, {H{\aa}kan } and Kaashoek, {Marinus A. } and Rodr{\'i}guez, {Alfonso Montes } and Treil, {Sergei }",
booktitle = "Concrete operators, spectral theory, operators in harmonic analysis and approximation",
}
RIS
TY - GEN
T1 - Crystal frameworks, matrix-valued functions and rigidity operators
AU - Power, Stephen
PY - 2014
Y1 - 2014
N2 - An introduction and survey is given of some recent work on the infinitesimal dynamics of crystal frameworks, that is, of translationally periodic discrete bond-node structures in ℝd, for d = 2,3,... We discuss the rigidity matrix, a fundamental object from finite bar-joint framework theory, rigidity operators, matrix-function representations and low energy phonons. These phonons in material crystals, such as quartz and zeolites, are known as rigid unit modes, or RUMs, and are associated with the relative motions of rigid units, such as SiO4 tetrahedra in the tetrahedral polyhedral bondnode model for quartz. We also introduce semi-infinite crystal frameworks, bi-crystal frameworks and associated multi-variable Toeplitz operators.
AB - An introduction and survey is given of some recent work on the infinitesimal dynamics of crystal frameworks, that is, of translationally periodic discrete bond-node structures in ℝd, for d = 2,3,... We discuss the rigidity matrix, a fundamental object from finite bar-joint framework theory, rigidity operators, matrix-function representations and low energy phonons. These phonons in material crystals, such as quartz and zeolites, are known as rigid unit modes, or RUMs, and are associated with the relative motions of rigid units, such as SiO4 tetrahedra in the tetrahedral polyhedral bondnode model for quartz. We also introduce semi-infinite crystal frameworks, bi-crystal frameworks and associated multi-variable Toeplitz operators.
KW - Rigidity operator
U2 - 10.1007/978-3-0348-0648-0_26
DO - 10.1007/978-3-0348-0648-0_26
M3 - Conference contribution/Paper
SN - 9783034806473
T3 - Operator Theory: Advances and Applications
SP - 405
EP - 420
BT - Concrete operators, spectral theory, operators in harmonic analysis and approximation
A2 - Boiso, Manuel Cepedello
A2 - Hedenmalm, Håkan
A2 - Kaashoek, Marinus A.
A2 - Rodríguez, Alfonso Montes
A2 - Treil, Sergei
PB - Springer
CY - Basel
ER -
