Mathematics, Department of


Date of this Version



2019 by the Tusi Mathematical Research Group


Banach J. Math. Anal. 13 (2019), no. 1, 192{216 ISSN: 1735-8787 (electronic)


In this article, we establish the Cameron{Martin translation theo- rems for the analytic Fourier{Feynman transform of functionals on the product function space C2 a;b[0; T]. The function space Ca;b[0; T] is induced by the gener- alized Brownian motion process associated with continuous functions a(t) and b(t) on the time interval [0; T]. The process used here is nonstationary in time and is subject to a drift a(t). To study our translation theorem, we introduce a Fresnel-type class Fa;b A1;A2 of functionals on C2 a;b[0; T], which is a generaliza- tion of the Kallianpur and Bromley{Fresnel class FA1;A2 . We then proceed to establish the translation theorems for the functionals in Fa;b A1;A2 .