Group ring elements with large spectral density
arXiv:1409.3212 · doi:10.1007/s00208-015-1170-7
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.
19 pages, v3: Changes suggested by a referee; Essentially this is the version published in Math. Ann
References in corpus (6)
- L2-determinant class and approximation of L2-Betti numbers
- Rational group ring elements with kernels having irrational dimension
- The spectral measure of certain elements of the complex group ring of a wreath product
- On Turing dynamical systems and the Atiyah problem
- Free Lamplighter Groups and a Question of Atiyah
- On the spectrum of lamplighter groups and percolation clusters