Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transformation theory and Christoffel formulas for matrix biorthogonal
  polynomials on the real line   In this paper transformations for matrix orthogonal polynomials in the real
line are studied. The orthogonality is understood in a broad sense, and is
given in terms of a nondegenerate continuous sesquilinear form, which in turn
is determined by a quasidefinite matrix of bivariate generalized functions with
a well defined support. The discussion of the orthogonality for such a
sesquilinear form includes, among others, matrix Hankel cases with linear
functionals, general matrix Sobolev orthogonality and discrete orthogonal
polynomials with an infinite support. The first transformation considered is
that of Geronimus type, two different methods are developed. A spectral one,
based on the spectral properties of the perturbing polynomial, and constructed
in terms of the second kind functions. Then, using spectral techniques and
spectral jets, Christoffel-Geronimus formulas for the transformed polynomials
and norms are presented. For this type of transformations, the paper also
proposes an alternative method, which does not require of spectral techniques.
A discussion on matrix spectral linear transformations is presented, as well.
These transformations can be understood as rational perturbations of the matrix
of bivariate generalized functions together with an addition of appropriate
masses, determined these last ones by the spectral properties of the polynomial
denominator. As for the Geronimus case, two techniques are applied, spectral
and mixed spectral/nonspectral. Christoffel--Geronimus--Uvarov formulas are
found with both approaches and some applications are given. The transformation
theory is finally discussed in the context of the 2D non-Abelian Toda lattice
and noncommutative KP hierarchies, understood as the theory of continuous
transformations of quasidefinite sesquilinear forms. This approach allows for
the finding of perturbed quasitau and Baker matrices.

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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: cs