Estimates for spectral density functions of matrices over $\mathbb{C}[\mathbb{Z}^d]$

Lück, Wolfgang

Estimates for spectral density functions of matrices over

ℂ [ℤ^{d}]

[Estimation de fonctions de densité spectrale de matrices de

ℂ [ℤ^{d}]

]

Lück, Wolfgang

Annales mathématiques Blaise Pascal, Tome 22 (2015), p. 73-88 / Harvested from Numdam

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Résumé
Abstract

Nous donnons une estimation polynomiale pour la fonction de densité spectrale d’une matrice sur l’algèbre complexe du groupe $ℤ^{d}$ . Ce résultat donne une borne inférieure explicite à l’invariant de Novikov-Shubin associé à la matrice, montrant en particulier que l’invariant de Novikov-Shubin est strictement positif.

We give a polynomial bound on the spectral density function of a matrix over the complex group ring of $ℤ^{d}$ . It yields an explicit lower bound on the Novikov-Shubin invariant associated to this matrix showing in particular that the Novikov-Shubin invariant is larger than zero.

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/ambp.346
Classification: 46L99, 58J50
Mots clés: Invariants de Novikov-Shubin, fonction de densité spectrale

@article{AMBP_2015__22_1_73_0,
     author = {L\"uck, Wolfgang},
     title = {Estimates for spectral density functions of matrices over $\mathbb{C}[\mathbb{Z}^d]$},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {22},
     year = {2015},
     pages = {73-88},
     doi = {10.5802/ambp.346},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2015__22_1_73_0}
}

Lück, Wolfgang. Estimates for spectral density functions of matrices over $\mathbb{C}[\mathbb{Z}^d]$. Annales mathématiques Blaise Pascal, Tome 22 (2015) pp. 73-88. doi : 10.5802/ambp.346. http://gdmltest.u-ga.fr/item/AMBP_2015__22_1_73_0/

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