Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gabor frames with rational density   We consider the frame property of the Gabor system G(g, {\alpha}, {\beta}) =
{e2{\pi}i{\beta}nt g(t - {\alpha}m) : m, n \in Z} for the case of rational
oversampling, i.e. {\alpha}, {\beta} \in Q. A 'rational' analogue of the
Ron-Shen Gramian is constructed, and prove that for any odd window function g
the system G(g, {\alpha}, {\beta}) does not generate a frame if {\alpha}{\beta}
= (n-1)/n. Special attention is paid to the first Hermite function h_1(t) =
te^(-{\pi}t^2).

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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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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: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom