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- Annales mathématiques Blaise Pascal

- Tome 22 (2015)

- no. 1

- p. 73-88

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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.

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.

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Lück, Wolfgang 1

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