Abstract
We prove that the densities of the semi-groups of order α, 0 < α < 1 associated with differential operators of second order and of divergence type, and the density of Riesz semi-groups of order α are comparables.
We give a necessary and sufficient condition such that the semi-group of order α and its resolvent family and their perturbated with a nonnegative and regular Radon measure are comparables.
When α = 1, we prove that the semi-group of brownian motion and its perturbated with a radial and nonnegative measure are comparables if and only if the measure generates a bounded potential, but the result is not true if the measure is not radial.
Ce travail est soutenu par la Fondation Nationale pour la Recherche Scientifique.
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Selmi, M. (1994). Comparaison des semi-groupes et des résolvantes d’ordre α associés à des opérateurs différentiels de type divergence. In: Bertin, E. (eds) ICPT ’91. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1118-8_2
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DOI: https://doi.org/10.1007/978-94-011-1118-8_2
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