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Transactions of the American Mathematical Society

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Nonautonomous Kato classes of measures and Feynman-Kac propagators

Author: Archil Gulisashvili
Journal: Trans. Amer. Math. Soc. 357 (2005), 4607-4632
MSC (2000): Primary 35K15; Secondary 60H30
Published electronically: December 9, 2004
MathSciNet review: 2156723
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Abstract: The behavior of the Feynman-Kac propagator corresponding to a time-dependent measure on $R^n$ is studied. We prove the boundedness of the propagator in various function spaces on $R^n$, and obtain a uniqueness theorem for an exponentially bounded distributional solution to a nonautonomous heat equation.

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Additional Information

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

Keywords: Nonautonomous heat equation, classes of time-dependent measures, Feynman-Kac propagators, time-dependent additive functionals
Received by editor(s): October 10, 2003
Received by editor(s) in revised form: December 22, 2003
Published electronically: December 9, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.