Nonautonomous Kato classes of measures and Feynman-Kac propagators

Gulisashvili, Archil

doi:10.1090/S0002-9947-04-03603-7

Nonautonomous Kato classes of measures and Feynman-Kac propagators
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by Archil Gulisashvili

Trans. Amer. Math. Soc. 357 (2005), 4607-4632

DOI: https://doi.org/10.1090/S0002-9947-04-03603-7

Published electronically: December 9, 2004

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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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