Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace Formulas and a Borg-type Theorem for CMV Operators with
  Matrix-valued Coefficients   We prove a general Borg-type inverse spectral result for a reflectionless
unitary CMV operator (CMV for Cantero, Moral, and Vel\'azquez) associated with
matrix-valued Verblunsky coefficients. More precisely, we find an explicit
formula for the Verblunsky coefficients of a reflectionless CMV matrix whose
spectrum consists of a connected arc on the unit circle. This extends a recent
result on CMV operators with scalar-valued coefficients. In the course of
deriving the Borg-type result we also use exponential Herglotz representations
of Caratheodory matrix-valued functions to prove an infinite sequence of trace
formulas connected with CMV operators.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex