Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A CMV connection between orthogonal polynomials on the unit circle and
  the real line   M. Derevyagin, L. Vinet and A. Zhedanov introduced in Constr. Approx. 36
(2012) 513-535 a new connection between orthogonal polynomials on the unit
circle and the real line. It maps any real CMV matrix into a Jacobi one
depending on a real parameter $\lambda$. These authors prove that this map
yields a natural link between the Jacobi polynomials on the unit circle and the
little and big $-1$ Jacobi polynomials on the real line. They also provide
explicit expressions for the measure and orthogonal polynomials associated with
the Jacobi matrix in terms of those related to the CMV matrix, but only for the
value $\lambda=1$ which simplifies the connection -basic DVZ connection-.
However, similar explicit expressions for an arbitrary value of $\lambda$ --
(general) DVZ connection -- are missing. This is the main problem overcome in
this paper.
  This work introduces a new approach to the DVZ connection which formulates it
as a two-dimensional eigenproblem by using known properties of CMV matrices.
This allows us to go further, providing explicit relations between the measures
and orthogonal polynomials for the general DVZ connection. It turns out that
this connection maps a measure on the unit circle into a rational perturbation
of an even measure supported on two symmetric intervals of the real line, which
reduce to a single interval for the basic DVZ connection, while the
perturbation becomes a degree one polynomial. Some instances of the DVZ
connection are shown to give new one-parameter families of orthogonal
polynomials on the real line.

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The categories of this paper are: eess
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio