Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kato classes for L\'evy processes   We prove that the definitions of the Kato class by the semigroup and by the
resolvent of the L\'{e}vy process on $\mathbb{R}^d$ coincide if and only if 0
is not regular for {0}. If 0 is regular for {0} then we describe both classes
in detail. We also give an analytic reformulation of these results by means of
the characteristic (L\'{e}vy-Khintchine) exponent of the process. The result
applies to the time-dependent (non-autonomous) Kato class. As one of the
consequences we obtain a simultaneous time-space smallness condition equivalent
to the Kato class condition given by the semigroup.

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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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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: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys