Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A pair of commuting hypergeometric operators on the complex plane and
  bispectrality   We consider the standard hypergeometric differential operator $D$ regarded as
an operator on the complex plane $C$ and the complex conjugate operator
$\overline D$. These operators formally commute and are formally adjoint one to
another with respect to an appropriate weight. We find conditions when they
commute in the Nelson sense and write explicitly their joint spectral
decomposition. It is determined by a two-dimensional counterpart of the Jacobi
transform (synonyms: generalized Mehler--Fock transform, Olevskii transform).
We also show that the inverse transform is an operator of spectral
decomposition for a pair of commuting difference operators defined in terms of
shifts in imaginary direction.

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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph