Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness in $L^1(R)$ of discrete translates   We characterize, in terms of the Beurling-Malliavin density, the discrete
spectra $\Lambda\subset\R$ for which a generator exists, that is a function
$\phi\in L^1(\R)$ such that its $\Lambda$-translates $\phi(x-\lambda),
\lambda\in\Lambda$, span $L^1(\R)$. It is shown that these spectra coincide
with the uniqueness sets for certain analytic classes. We also present examples
of discrete spectra $\Lambda\subset\R$ which do not admit a single generator
while they admit a pair of generators.

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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin