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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Classes of time-dependent measures, non-homogeneous Markov processes, and Feynman-Kac propagators

Author: Archil Gulisashvili
Journal: Trans. Amer. Math. Soc. 360 (2008), 4063-4098
MSC (2000): Primary 47D08; Secondary 60J35
Published electronically: March 11, 2008
MathSciNet review: 2395164
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Abstract: We study the inheritance of properties of free backward propagators associated with transition probability functions by backward Feynman-Kac propagators corresponding to functions and time-dependent measures from non-autonomous Kato classes. The inheritance of the following properties is discussed: the strong continuity of backward propagators on the space $ L^r$, the $ (L^r-L^q)$-smoothing property of backward propagators, and various generalizations of the Feller property. We also prove that a propagator on a Banach space is strongly continuous if and only if it is separately strongly continuous and locally uniformly bounded.

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Archil Gulisashvili
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701

Keywords: Propagators and backward propagators, non-homogeneous Markov processes, non-autonomous Kato classes, free propagators, Feynman-Kac propagators, the Feller property, the inheritance problem.
Received by editor(s): March 27, 2006
Published electronically: March 11, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.