[Sur les propagateurs de Feynman–Kac pour l'équation de la chaleur avec un potentiel qui est une mesure dépendant du temps]
On étudie les propagateurs de Feynman–Kac, correspondant à l'équation de la chaleur dans le sens direct et inverse avec un potentiel qui est une mesure dépendant du temps. Nous considérons diverses généralisations de la classe de Kato de potentiels. Sous des conditions appropriées sur le potentiel nous obtenons les théorèmes de résolubilité et d'unicité pour l'équation de la chaleur avec un potentiel, et nous étudions les propriétés des transformations définies par les propagateurs.
The Feynman–Kac propagators, corresponding to the forward and backward heat equations with a time-dependent measure as a potential are studied. Various generalizations of the Kato class of potentials are considered. Under appropriate conditions on the potential, the solvability and uniqueness theorems for the heat equation with a potential are obtained, and the mapping properties of the Feynman–Kac propagators are discussed.
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Archil Gulisashvili 1
@article{CRMATH_2002__334_6_445_0,
author = {Archil Gulisashvili},
title = {Classes of time-dependent measures and the behavior of {Feynman{\textendash}Kac} propagators},
journal = {Comptes Rendus. Math\'ematique},
pages = {445--449},
publisher = {Elsevier},
volume = {334},
number = {6},
year = {2002},
doi = {10.1016/S1631-073X(02)02294-X},
language = {en},
}
Archil Gulisashvili. Classes of time-dependent measures and the behavior of Feynman–Kac propagators. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 445-449. doi : 10.1016/S1631-073X(02)02294-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02294-X/
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