Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering matrices and generalized Fourier transforms in long-range
  $N$-body problems   We give a definition of scattering matrices based on the asymptotic behaviors
of generalized eigenfunctions and show that these scattering matrices are
equivalent to the ones defined by wave-operator approach in long-range $N$-body
problems. We also define generalized Fourier transforms by the asymptotic
behaviors of outgoing solutions to nonhomogeneous equations and show that they
are equivalent to the definition using wave operators. We also prove that the
adjoint operators of the generalized Fourier transforms are given by Poisson
operators.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg