Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reflectionless CMV matrices and scattering theory   Reflectionless CMV matrices are studied using scattering theory. By changing
a single Verblunsky coefficient a full-line CMV matrix can be decoupled and
written as the sum of two half-line operators. Explicit formulas for the
scattering matrix associated to the coupled and decoupled operators are
derived. In particular, it is shown that a CMV matrix is reflectionless iff the
scattering matrix is off-diagonal which in turn provides a short proof of an
important result of [Breuer-Ryckman-Simon]. These developments parallel those
recently obtained for Jacobi matrices.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int