Spectral Analysis of the local Commutator Operators
| dc.creator | Burnol, Jean-Francois | |
| dc.date | 1998-12-01 | |
| dc.date.accessioned | 2026-07-07T05:27:05Z | |
| dc.date.available | 2026-07-07T05:27:05Z | |
| dc.description | The 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.description | 16 pages, plain TeX | |
| dc.identifier | https://arxiv.org/abs/math/9812012 | |
| dc.identifier | http://arxiv.org/abs/math/9812012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77790 | |
| dc.subject | Number Theory | |
| dc.subject | 11M06, 11R42 | |
| dc.title | Spectral Analysis of the local Commutator Operators | |
| dc.type | text |