Ruelle operators: Functions which are harmonic with respect to a transfer operator
| dc.creator | Jorgensen, Palle E. T. | |
| dc.date | 1998-05-29 | |
| dc.date.accessioned | 2026-07-07T05:24:53Z | |
| dc.date.available | 2026-07-07T05:24:53Z | |
| dc.description | Let $ N \in \mathbb{N} $, $ N \geq 2 $, be given. Motivated by wavelet analysis, we consider a class of normal representations of the $ C^* $-algebra $ \mathfrak{A}_{N} $ on two unitary generators $ U $, $ V $ subject to the relation \[ UVU^{-1}=V^{N}. \] The representations are in one-to-one correspondence with solutions $ h \in L^{1}(\mathbb{T}) $, $ h \geq 0 $, to $ R(h)=h $ where $ R $ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $ \mathfrak{A}_{N} $ may also be viewed as representations of a certain (discrete) $ N $-adic $ ax+b $ group which was considered recently by J.-B. Bost and A. Connes. | |
| dc.description | 56 pages, 4 figures (some with sub-figures), AMS-LaTeX v1.2r | |
| dc.identifier | https://arxiv.org/abs/math/9805141 | |
| dc.identifier | http://arxiv.org/abs/math/9805141 | |
| dc.identifier | Mem. Amer. Math. Soc. 152 (2001), no. 720, viii+60 pp. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76982 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L60, 47D25, 42A16, 43A65 (Primary); 46L45, 42A65, 41A15 (Secondary) | |
| dc.title | Ruelle operators: Functions which are harmonic with respect to a transfer operator | |
| dc.type | text |