Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier analysis and holomorphic decomposition on the one-sheeted
  hyperboloid   We prove a Cauchy-type integral representation for classes of functions
holomorphic in four priviledged tuboid domains of the complexified one-sheeted
two-dimensional hyperboloid. From a physical viewpoint, this hyperboloid can be
used for describing both the two-dimensional de Sitter and anti-de Sitter
universes. For two of these tuboids, called ``the Lorentz tuboids'' and
relevant for de Sitter Quantum Field Theory, the boundary values onto the real
hyperboloid of functions holomorphic in these domains admit continuous
Fourier-Helgason-type transforms. For the other two tuboids, called the
``chiral tuboids'' and relevant for anti-de Sitter Quantum Field Theory, the
boundary values on the reals of functions holomorphic in these domains admit
discrete Fourier-Helgason-type transforms. In both cases, the inversion
formulae for these transformations are derived by using the previous Cauchy
representation for the respective classes of functions. The decomposition of
functions on the real hyperboloid into sums of boundary values of holomorphic
functions from the previous four tuboids gives a complete and explicit
treatment of the Gelfand-Gindikin program for the one-sheeted hyperboloid.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph