Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear spectral transformations for multivariate orthogonal polynomials
  and multispectral Toda hierarchies   Linear spectral transformations of orthogonal polynomials in the real line,
and in particular Geronimus transformations, are extended to orthogonal
polynomials depending on several real variables. Multivariate
Christoffel-Geronimus-Uvarov formulae for the perturbed orthogonal polynomials
and their quasi-tau matrices are found for each perturbation of the original
linear functional. These expressions are given in terms of quasi-determinants
of bordered truncated block matrices and the 1D Christoffel-Geronimus-Uvarov
formulae in terms of quotient of determinants of combinations of the original
orthogonal polynomials and their Cauchy transforms, are recovered. A new
multispectral Toda hierarchy of nonlinear partial differential equations, for
which the multivariate orthogonal polynomials are reductions, is proposed. This
new integrable hierachy is associated with non-standard multivariate
biorthogonality. Wave and Baker functions, linear equations, Lax and
Zakharov-Shabat equations, KP type equations, appropriate reductions,
Darboux/linear spectral transformations, and bilinear equations involving
linear spectral transformations are presented.

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The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th