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

Wolfgang Lück

doi:10.5802/ambp.346

Estimates for spectral density functions of matrices over

ℂ [ℤ^{d}]

[Estimation de fonctions de densité spectrale de matrices de

ℂ [ℤ^{d}]

]

Wolfgang Lück ¹

¹ Mathematicians Institut der Universität Bonn Endenicher Allee 60 53115 Bonn, Germany

Annales mathématiques Blaise Pascal, Tome 22 (2015) no. 1, pp. 73-88.

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.

DOI : 10.5802/ambp.346

Classification : 46L99, 58J50
Keywords: spectral density function, Novikov-Shubin invariants
Mot clés : Invariants de Novikov-Shubin, fonction de densité spectrale

Affiliations des auteurs :

Wolfgang Lück ¹

¹ Mathematicians Institut der Universität Bonn Endenicher Allee 60 53115 Bonn, Germany

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Wolfgang Lück. Estimates for spectral density functions of matrices over $\mathbb{C}[\mathbb{Z}^d]$. Annales mathématiques Blaise Pascal, Tome 22 (2015) no. 1, pp. 73-88. doi : 10.5802/ambp.346. https://ambp.centre-mersenne.org/articles/10.5802/ambp.346/

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