Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolvent at low energy and Riesz transform for Schrodinger operators on
  asymptotically conic manifolds, I   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 $1<p<n$ 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.

29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys