Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A weighted estimate for two dimensional Schrodinger, matrix schrodinger
  and wave equations with resonance of first kind at zero energy   We study the two dimensional Schr\"odinger operator, $H=-\Delta+V$, in the
weighted L^1(\R^2) \rightarrow L^{\infty}(\R^2) setting when there is a
resonance of the first kind at zero energy. In particular, we show that if
|V(x)|\les \la x \ra ^{-3-} and there is only s-wave resonance at zero of H,
then \big\| w^{-1} \big( e^{itH}P_{ac} f - {\f 1 t } F f \big) \big\| _{\infty}
\leq \frac {C} {|t| (\log|t|)^2 } \|wf\|_1 |t|>2, with w(x)=\log^2(2+|x|). Here
Ff=c \psi\la f,\psi \ra, where \psi is an s-wave resonance function. We also
extend this result to matrix Schr\"odinger and wave equations with potentials
under similar conditions.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat