Resolvent at low energy and Riesz transform for Schrodinger operators on asymptotically conic manifolds, I

Details Resolvent at low energy and Riesz transform for Schrodinger operators on asymptotically conic manifolds, I Resolvent at low energy and Riesz transform for Schrodinger operators on asymptotically conic manifolds, I

2007-01-18

arxiv.org/abs/math/0701515v1

Mathematics

Analysis of PDEs

28 pages, 1 figure

Scientific paper

We analyze the resolvent $R(k)=(P+k^2)^{-1}$ of Schr\"odinger operators $P=\Delta+V$ 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

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