Spectral Analysis of the local Commutator Operators

dc.creatorBurnol, Jean-Francois
dc.date1998-12-01
dc.date.accessioned2026-07-07T05:27:05Z
dc.date.available2026-07-07T05:27:05Z
dc.descriptionThe spectral analysis of the (local) conductor operator H = log(|q|) + log(|p|) was shown in a previous paper to be given by the Explicit Formula. I give here the spectral analysis of the commutator operator K = i[log(|p|),log(|q|)] (which shares with H the property of complete dilation invariance). Its spectral function is found to be the derivative of the one of H. It is then deduced that K anticommutes with the Inversion and is a bounded operator. Higher commutators are related in the same manner to the higher derivatives of the Gamma function, which thus all acquire an operator theoretic and spectral interpretation.
dc.description16 pages, plain TeX
dc.identifierhttps://arxiv.org/abs/math/9812012
dc.identifierhttp://arxiv.org/abs/math/9812012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77790
dc.subjectNumber Theory
dc.subject11M06, 11R42
dc.titleSpectral Analysis of the local Commutator Operators
dc.typetext

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