Smoothness and high energy asymptotics of the spectral shift function in many-body scattering
| dc.creator | Vasy, Andras | |
| dc.creator | Wang, Xue-Ping | |
| dc.date | 2001-06-25 | |
| dc.date.accessioned | 2026-07-07T04:42:18Z | |
| dc.date.available | 2026-07-07T04:42:18Z | |
| dc.description | Let H=Δ+\sum_{#a=2} V_a be a 3-body Hamiltonian, H_a the subsystem Hamiltonians, Δthe positive Laplacian of the Euclidean metric on X_0=R^n, V_a real-valued. Buslaev and Merkurev have shown that, if the pair potentials decay sufficiently fast, for ϕsmooth and compactly supported, the operator ϕ(H)-ϕ(H_0)-\sum_{#a=2}(ϕ(H_a)-ϕ(H_0)) is trace class. Hence, one can define a modified spectral shift function σ, as a distribution on R, by taking its trace. In this paper we show that if V_a are Schwartz, then σis in fact smooth away from the thresholds, and obtain its high energy asymptotics. In addition, we generalize this result to N-body scattering, N arbitrary. | |
| dc.description | 30 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0106209 | |
| dc.identifier | http://arxiv.org/abs/math/0106209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61723 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | Spectral Theory | |
| dc.subject | 35P25 (Primary) 47A40, 81U10 (Secondary) | |
| dc.title | Smoothness and high energy asymptotics of the spectral shift function in many-body scattering | |
| dc.type | text |