Year: 2017
Type: article
Abstract: We prove that the definitions of the Kato class through the semigroup and through the resolvent of the Lévy process in $\mathbb {R}^{d}$ 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 (Lévy-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.
Source: Potential Analysis
Authors: Tomasz Grzywny, Karol Szczypkowski
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W2163285969