Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit formula for Schroedinger wave operators on the half-line for
  potentials up to optimal decay   We give an explicit formula for the wave operators for Schroedinger operators
on the half-line with a potential decaying strictly faster than the polynomial
of degree minus two. The formula consists of the main term given by the
scattering operator and a function of the generator of the dilation group, and
a Hilbert-Schmidt remainder term. Our method is based on the elementary
construction of the generalized Fourier transform in terms of the solutions of
the Volterra integral equations. As a corollary, a topological interpretation
of Levinson's theorem is established via an index theorem approach.

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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex