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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

General gauge theorem for multiplicative functionals


Authors: K. L. Chung and K. M. Rao
Journal: Trans. Amer. Math. Soc. 306 (1988), 819-836
MSC: Primary 60J40; Secondary 60J57
MathSciNet review: 933320
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Abstract: We generalize our previous work on the gauge theorem and its various consequences and complements, initiated in [8] and somewhat extended by subsequent investigations (see [6]). The generalization here is two-fold. First, instead of the Brownian motion, the underlying process is now a fairly broad class of Markov processes, not necessarily having continuous paths. Second, instead of the Feynman-Kac functional, the exponential of a general class of additive functionals is treated. The case of Schrödinger operator $ \Delta /2 + \nu $, where $ \nu $ is a suitable measure, is a simple special case. The most general operator, not necessarily a differential one, which may arise from our potential equations is briefly discussed toward the end of the paper. Concrete instances of applications in this case should be of great interest.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0933320-1
PII: S 0002-9947(1988)0933320-1
Article copyright: © Copyright 1988 American Mathematical Society