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• W3100987860 abstract "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." @default.
• W3100987860 created "2020-11-23" @default.
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• W3100987860 date "2017-01-26" @default.
• W3100987860 modified "2023-10-10" @default.
• W3100987860 title "Kato Classes for Lévy Processes" @default.
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• W3100987860 doi "https://doi.org/10.1007/s11118-017-9614-1" @default.
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