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Contents of PMS, Vol. 21, Fasc. 2,
pages 381 - 404
 

ONE-DIMENSIONAL SYMMETRIC STABLE FEYNMAN-KAC SEMIGROUPS

H. Byczkowska
T. Byczkowski

Abstract: We investigate here one-dimensional Feynman-Kac semigroups based on symmetric a -stable processes. We begin with establishing the properties of Green operators of intervals and halflines on functions from the Kato class. Then we provide a sufficient condition for gaugeability of the halfline (- oo , b) and evaluate the critical value b.

1991 AMS Mathematics Subject Classification: Primary 31B25, 60J50.

Key words and phrases: a -stable Lévy processes, Feynman-Kac semigroups on R1, potential theory, Kato class, Green operators, gauge function, gaugeability.

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