Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Rank Decoupling of Full-Lattice CMV Operators with Scalar- and
  Matrix-Valued Verblunsky Coefficients   Relations between half- and full-lattice CMV operators with scalar- and
matrix-valued Verblunsky coefficients are investigated. In particular, the
decoupling of full-lattice CMV operators into a direct sum of two half-lattice
CMV operators by a perturbation of minimal rank is studied. Contrary to the
Jacobi case, decoupling a full-lattice CMV matrix by changing one of the
Verblunsky coefficients results in a perturbation of twice the minimal rank.
The explicit form for the minimal rank perturbation and the resulting two
half-lattice CMV matrices are obtained. In addition, formulas relating the
Weyl--Titchmarsh $m$-functions (resp., matrices) associated with the involved
CMV operators and their Green's functions (resp., matrices) are derived.

0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg