Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$ Properties of L\'{e}vy Generators on Compact Riemannian Manifolds   We consider isotropic L\'evy processes on a compact Riemannian manifold,
obtained from an $\mathbb{R}^d$-valued L\'evy process through rolling without
slipping. We prove that the Feller semigroups associated with these processes
extend to strongly continuous contraction semigroups on $L^p$, for $1\leq
p<\infty$, and that they are self-adjoint when $p=2$. When the motion has a
non-trivial Brownian part, we prove that the generator has a discrete spectrum
of eigenvalues and that the semigroup is trace-class.

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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: eess