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Group ring elements with large spectral density

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Group ring elements with large spectral density. / Grabowski, Łukasz.
In: Mathematische Annalen, Vol. 363, No. 1, 01.10.2015, p. 637-656.

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

Harvard

Grabowski, Ł 2015, 'Group ring elements with large spectral density', Mathematische Annalen, vol. 363, no. 1, pp. 637-656. https://doi.org/10.1007/s00208-015-1170-7

APA

Grabowski, Ł. (2015). Group ring elements with large spectral density. Mathematische Annalen, 363(1), 637-656. https://doi.org/10.1007/s00208-015-1170-7

Vancouver

Grabowski Ł. Group ring elements with large spectral density. Mathematische Annalen. 2015 Oct 1;363(1):637-656. Epub 2015 Feb 17. doi: 10.1007/s00208-015-1170-7

Author

Grabowski, Łukasz. / Group ring elements with large spectral density. In: Mathematische Annalen. 2015 ; Vol. 363, No. 1. pp. 637-656.

Bibtex

@article{845d65f143454f499163c5582102e2d1,
title = "Group ring elements with large spectral density",
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.",
keywords = "20C07 , 20F65, 57M10",
author = "{\L}ukasz Grabowski",
year = "2015",
month = oct,
day = "1",
doi = "10.1007/s00208-015-1170-7",
language = "English",
volume = "363",
pages = "637--656",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "1",

}

RIS

TY - JOUR

T1 - Group ring elements with large spectral density

AU - Grabowski, Łukasz

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

KW - 20C07

KW - 20F65

KW - 57M10

U2 - 10.1007/s00208-015-1170-7

DO - 10.1007/s00208-015-1170-7

M3 - Journal article

VL - 363

SP - 637

EP - 656

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1

ER -