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Group ring elements with large spectral density

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
<mark>Journal publication date</mark>1/10/2015
<mark>Journal</mark>Mathematische Annalen
Issue number1
Volume363
Number of pages20
Pages (from-to)637-656
Publication StatusPublished
Early online date17/02/15
<mark>Original language</mark>English

Abstract

Given δ>0δ>0 we construct a group GG and a group ring element S∈Z[G]S∈Z[G] such that the spectral measure μμ of SS fulfils μ((0,ε))>C|log(ε)|1+δμ((0,ε))>C|log⁡(ε)|1+δ for small εε. In particular the Novikov-Shubin invariant of any such SS is 00. The constructed examples show that the best known upper bounds on μ((0,ε))μ((0,ε)) are not far from being optimal.