Projective Pseudodifferential Analysis and Harmonic Analysis
| dc.creator | Pevzner, Michael | |
| dc.creator | Unterberger, André | |
| dc.date | 2006-05-05 | |
| dc.date.accessioned | 2026-07-07T07:13:56Z | |
| dc.date.available | 2026-07-07T07:13:56Z | |
| dc.description | We consider pseudodifferential operators on functions on $\R^{n+1}$ which commute with the Euler operator, and can thus be restricted to spaces of functions homogeneous of some given degree. Their symbols can be regarded as functions on a reduced phase space, isomorphic to the homogeneous space $G_n/H_n=SL(n+1,\R)/GL(n,\R)$, and the resulting calculus is a pseudodifferential analysis of operators acting on spaces of appropriate sections of line bundles over the projective space $P_n(\R)$ : these spaces are the representation spaces of the maximal degenerate series $(π_{iλ,ε})$ of $G_n$ . This new approach to the quantization of $G_n/H_n$, already considered by other authors, has several advantages: as an example, it makes it possible to give a very explicit version of the continuous part from the decomposition of $L^2(G_n/H_n)$ under the quasiregular action of $G_n$ . We also consider interesting special symbols, which arise from the consideration of the resolvents of certain infinitesimal operators of the representation $π_{iλ,ε}$ . | |
| dc.identifier | https://arxiv.org/abs/math/0605143 | |
| dc.identifier | http://arxiv.org/abs/math/0605143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112671 | |
| dc.subject | Representation Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 47G30, 22E46, 43A85 | |
| dc.title | Projective Pseudodifferential Analysis and Harmonic Analysis | |
| dc.type | text |