Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bilinear biorthogonal expansions and the Dunkl kernel on the real line   We study an extension of the classical Paley-Wiener space structure, which is
based on bilinear expansions of integral kernels into biorthogonal sequences of
functions. The structure includes both sampling expansions and Fourier-Neumann
type series as special cases, and it also provides a bilinear expansion for the
Dunkl kernel (in the rank 1 case) which is a Dunkl analogue of Gegenbauer's
expansion of the plane wave and the corresponding sampling expansions. In fact,
we show how to derive sampling and Fourier-Neumann type expansions from the
results related to the bilinear expansion for the Dunkl kernel.

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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci