Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat kernel analysis for Bessel operators on symmetric cones   We investigate the heat equation corresponding to the Bessel operators on a
symmetric cone $\Omega=G/K$. These operators form a one-parameter family of
elliptic self-adjoint second order differential operators and occur in the Lie
algebra action of certain unitary highest weight representations. The heat
kernel is explicitly given in terms of a multivariable $I$-Bessel function on
$\Omega$. Its corresponding heat kernel transform defines a continuous linear
operator between $L^p$-spaces. The unitary image of the $L^2$-space under the
heat kernel transform is characterized as a weighted Bergmann space on the
complexification $G_{\mathbb C}/K_{\mathbb C}$ of $\Omega$, the weight being
expressed explicitly in terms of a multivariable $K$-Bessel function on
$\Omega$. Even in the special case of the symmetric cone $\Omega=\mathbb{R}_+$
these results seem to be new.

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The categories of this paper are: hep-ex
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The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat