Resolvent at low energy and Riesz transform for Schrodinger operators on asymptotically conic manifolds, I
| dc.creator | Guillarmou, Colin | |
| dc.creator | Hassell, Andrew | |
| dc.date | 2007-01-18 | |
| dc.date.accessioned | 2026-07-07T07:41:43Z | |
| dc.date.available | 2026-07-07T07:41:43Z | |
| dc.description | We analyze the resolvent $R(k)=(P+k^2)^{-1}$ of Schrödinger operators $P=Δ+V$ with short range potential $V$ on asymptotically conic manifolds $(M,g)$ (this setting includes asymptotically Euclidean manifolds) near $k=0$. We make the assumption that the dimension is greater or equal to 3 and that $P$ has no $L^2$ null space and no resonance at 0. In particular, we show that the Schwartz kernel of $R(k)$ is a conormal polyhomogeneous distribution on a desingularized version of $M\times M\times [0,1]$. Using this, we show that the Riesz transform of $P$ is bounded on $L^p$ for $1<p<n$ and that this range is optimal if $V$ is not identically zero or if $M$ has more than one end. We also analyze the case V=0 with one end. In a follow-up paper, we shall deal with the same problem in the presence of zero modes and zero-resonances. | |
| dc.description | 28 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0701515 | |
| dc.identifier | http://arxiv.org/abs/math/0701515 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122217 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 35J10, 58J37 | |
| dc.title | Resolvent at low energy and Riesz transform for Schrodinger operators on asymptotically conic manifolds, I | |
| dc.type | text |