In this article, we establish the Cameron–Martin translation theorems for the analytic Fourier–Feynman transform of functionals on the product function space . The function space is induced by the generalized Brownian motion process associated with continuous functions and on the time interval . The process used here is nonstationary in time and is subject to a drift . To study our translation theorem, we introduce a Fresnel-type class of functionals on , which is a generalization of the Kallianpur and Bromley–Fresnel class . We then proceed to establish the translation theorems for the functionals in .
"Translation theorems for the Fourier–Feynman transform on the product function space ." Banach J. Math. Anal. 13 (1) 192 - 216, January 2019. https://doi.org/10.1215/17358787-2018-0022