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Crystal frameworks, matrix-valued functions and rigidity operators

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNConference contribution/Paperpeer-review

Published

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/ISSNConference contribution/Paperpeer-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). https://doi.org/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 -