Group ring elements with large spectral density
Group Theory
2015-04-27 v3 Geometric Topology
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.
Cite
@article{arxiv.1409.3212,
title = {Group ring elements with large spectral density},
author = {Łukasz Grabowski},
journal= {arXiv preprint arXiv:1409.3212},
year = {2015}
}
Comments
19 pages, v3: Changes suggested by a referee; Essentially this is the version published in Math. Ann