Around a Sobolev-Orlicz inequality for operators of given spectral density

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dc.creatorRumin, Michel
dc.date2009-02-16
dc.date.accessioned2026-07-07T12:42:16Z
dc.date.available2026-07-07T12:42:16Z
dc.descriptionWe prove some general Sobolev-Orlicz, Nash and Faber-Krahn inequalities for positive operators of given ultracontractive norms of the spectral projectors on ]0, lambda]. For invariant operators on coverings of finite simplicial complexes this "ultracontractive spectral decay" is equivalent to von-Neumann's spectral density function. This allows in the polynomial decay case to relate the Novikov-Shubin numbers of such coverings to Sobolev inequalities on exact $\ell^2$-cochains, and to the vanishing of the torsion of the $\ell^{p,2}$-cohomology for some $p \geq 2$.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0902.2690
dc.identifierhttp://arxiv.org/abs/0902.2690
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220017
dc.subjectSpectral Theory
dc.subjectFunctional Analysis
dc.subject58J50; 46E35; 58J35; 46E30; 35P20
dc.titleAround a Sobolev-Orlicz inequality for operators of given spectral density
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