Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp time decay estimates for the discrete Klein-Gordon equation   We establish sharp time decay estimates for the the Klein-Gordon equation on
the cubic lattice in dimensions $d=2,3,4$. The $\ell^1\to\ell^{\infty}$
dispersive decay rate is $|t|^{-3/4}$ for $d=2$, $|t|^{-7/6}$ for $d=3$ and
$|t|^{-3/2}\log|t|$ for $d=4$. These decay rates are faster than conjectured by
Kevrekidis and Stefanov (2005). The proof relies on oscillatory integral
estimates and proceeds by a detailed analysis of the the singularities of the
associated phase function. We also prove new Strichartz estimates and discuss
applications to nonlinear PDEs and spectral theory.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph