%0 Journal Article
%T Spectral distribution and L2-isoperimetric profile of Laplace operators on groups
%+ Mathematical Institute, University of Wroclaw
%+ Interdisciplinary Scientific Center Poncelet (ISCP)
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%+ University of Chicago
%+ Universität Regensburg (UR)
%A Bendikov, Alexander
%A Pittet, Christophe
%A Sauer, Roman
%Z A. Bendikov was supported by the University of Aix-Marseille I as an invited Professor and by the Polish Government Scientific Research Fund, Grant NN201371736. Ch. Pittet was supported by the CNRS and the Marie Curie Transfer of Knowledge Fellowship of the European Community’s Sixth Framework Program under contract number MTKD-CT-2004-013389 with the University of Wroclaw. A. Bendikov and Ch. Pittet are grateful to Prof. E. Damek who managed the ToK contract, and to Prof. A. Grigor’yan for an invitation at the University of Bielefeld. They are also grateful to the Erwin Schrödinger Institute for several invitations. R. Sauer was supported by DFG Grant SA 1661/1-2. All authors are grateful for the financial support from Prof. W. Lück’s Leibniz award for a meeting at the WWU Münster.
%Z 22 pages; changed title; improved exposition and gave more details in some of the proofs.To the memory of Andrzej Hulanicki.
%< avec comité de lecture
%@ 0025-5831
%J Mathematische Annalen
%I Springer Verlag
%V 354
%N 1
%P 43-72
%8 2012-09
%D 2012
%Z 0901.0271
%R 10.1007/s00208-011-0724-6
%K amenable group
%K spectral distribution
%K solvable group
%K geometric group theory
%K Laplace operator
%K exponential growth
%K sharp estimate
%Z 58J35, 20F63; 60G50
%Z Mathematics [math]/Group Theory [math.GR]
%Z Mathematics [math]/Spectral Theory [math.SP]Journal articles
%X We give a formula relating the $L^2$-isoperimetric profile to the spectral distribution of the Laplace operator associated to a finitely generated group $\Gamma$ or a Riemannian manifold with a cocompact, isometric $\Gamma$-action. As a consequence, we can apply techniques from geometric group theory to estimate the spectral distribution of the Laplace operator in terms of the growth and the F{\o}lner's function of the group, generalizing previous estimates by Gromov and Shubin. This leads, in particular, to sharp estimates of the spectral distributions for several classes of solvable groups. Furthermore, we prove the asymptotic invariance of the spectral distribution under changes of measures with finite second moment.
%G English
%2 https://hal.science/hal-01305024/document
%2 https://hal.science/hal-01305024/file/0901.0271.pdf
%L hal-01305024
%U https://hal.science/hal-01305024
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE