Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bessel convolutions on matrix cones   In this paper we introduce probability-preserving convolution algebras on
cones of positive semidefinite matrices over one of the division algebras $\b F
= \b R, \b C$ or $\b H$ which interpolate the convolution algebras of radial
bounded Borel measures on a matrix space $M_{p,q}(\b F)$ with $p\geq q$.
Radiality in this context means invariance under the action of the unitary
group $U_p(\b F)$ from the left. We obtain a continuous series of commutative
hypergroups whose characters are given by Bessel functions of matrix argument.
Our results generalize well-known structures in the rank one case, namely the
Bessel-Kingman hypergroups on the positive real line, to a higher rank setting.
In a second part of the paper, we study structures depending only on the matrix
spectra. Under the mapping $r\mapsto \text{spec}(r)$, the convolutions on the
underlying matrix cone induce a continuous series of hypergroup convolutions on
a Weyl chamber of type $B_q$. The characters are now Dunkl-type Bessel
functions. These convolution algebras on the Weyl chamber naturally extend the
harmonic analysis for Cartan motion groups associated with the Grassmann
manifolds $U(p,q)/(U_p\times U_q)$ over $\b F$.

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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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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: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat