Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterisations of Fourier and Fourier--Stieltjes algebras on locally
  compact groups   Motivated by the beautiful work of M. A. Rieffel (1965) and of M. E. Walter
(1974), we obtain characterisations of the Fourier algebra $A(G)$ of a locally
compact group $G$ in terms of the class of $F$-algebras (i.e. a Banach algebra
$A$ such that its dual $A'$ is a $W^*$-algebra whose identity is multiplicative
on $A$). For example, we show that the Fourier algebras are precisely those
commutative semisimple $F$-algebras that are Tauberian, contain a nonzero real
element, and possess a dual semigroup that acts transitively on their
spectrums. Our characterisations fall into three flavours, where the first one
will be the basis of the other two. The first flavour also implies a simple
characterisation of when the predual of a Hopf-von Neumann algebra is the
Fourier algebra of a locally compact group. We also obtain similar
characterisations of the Fourier--Stieltjes algebras of $G$. En route, we prove
some new results on the problem of when a subalgebra of $A(G)$ is the whole
algebra and on representations of discrete groups.

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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int