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arXiv · 1409.3212

Group ring elements with large spectral density

Łukasz Grabowski
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Abstract

Given an arbitrary d>0 we construct a group G and a group ring element S in Z[G] such that the spectral measure mu of S has the property that mu((0,eps)) > C/|log(eps)|^(1+d) for small eps. In particular the Novikov-Shubin invariant of any such S is 0. The constructed examples show that the best known upper bounds on mu((0,eps)) are not far from being optimal.

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Łukasz Grabowski. 2015-04-24. Group ring elements with large spectral density. https://doi.org/10.1007/s00208-015-1170-7

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