Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Spherical $\pi$-Operator   In this article, we define the spherical $\pi$-operator over domains in the
$(n-1)$-D unit sphere $S^n$ of $R^n$ and develop new and analogous results on
the operator it self and its mapping properties. We introduce the spherical
Dirac operator $\Gamma_\alpha$ as an $\alpha$- shift of of $\Gamma_omega$,
where $\Gamma_omega$ is the negative of the wedge (or Grassmann) product of
$\omega$ with that of the Dirac operator $D_\omega$. A gegenbauer polynomial is
used as a Cauchy kernel for the spherical Dirac operator $\Gamma_alpha$.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: comp-gas