Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Published

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

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

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

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

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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",

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publisher = "Springer",

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editor = "Boiso, {Manuel Cepedello} and Hedenmalm, {H{\aa}kan } and Kaashoek, {Marinus A. } and Rodr{\'i}guez, {Alfonso Montes } and Treil, {Sergei }",

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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.

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DO - 10.1007/978-3-0348-0648-0_26

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A2 - Rodríguez, Alfonso Montes

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