Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersive Bounds for the three-dimensional Schrodinger equation with
  almost critical potentials   We prove a dispersive estimate for the time-independent Schrodinger operator
H = -\Delta + V in three dimensions. The potential V(x) is assumed to lie in
the intersection L^p(R^3) \cap L^q(R^3), p < 3/2 < q, and also to satisfy a
generic zero-energy spectral condition. This class, which includes potentials
that have pointwise decay |V(x)| < C(1+|x|)^{-2-\epsilon}, is nearly critical
with respect to the natural scaling of the Laplacian. No additional regularity,
decay, or positivity of V is assumed.

9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys