Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convolution kernels versus spectral multipliers for sub-Laplacians on
  groups of polynomial growth   Let $\mathcal{L}$ be a sub-Laplacian on a connected Lie group $G$ of
polynomial growth. It is well known that, if $F : \mathbb{R} \to \mathbb{C}$ is
in the Schwartz class $\mathcal{S}(\mathbb{R})$, then the convolution kernel
$\mathcal{K}_{F(\mathcal{L})}$ of the operator $F(\mathcal{L})$ is in the
Schwartz class $\mathcal{S}(G)$. Here we prove a sort of converse implication
for a class of groups $G$ including all solvable noncompact groups of
polynomial growth. We also discuss the problem whether integrability of
$\mathcal{K}_{F(\mathcal{L})}$ implies continuity of $F$.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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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: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph