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http://dx.doi.org/10.4134/JKMS.j170094

TRANSLATION THEOREMS FOR THE ANALYTIC FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PATHS ON WIENER SPACE  

Chang, Seung Jun (Department of Mathematics Dankook University)
Choi, Jae Gil (Department of Mathematics Dankook University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 147-160 More about this Journal
Abstract
In this article, we establish translation theorems for the analytic Fourier-Feynman transform of functionals in non-stationary Gaussian processes on Wiener space. We then proceed to show that these general translation theorems can be applied to two well-known classes of functionals; namely, the Banach algebra S introduced by Cameron and Storvick, and the space ${\mathcal{B}}^{(P)}_{\mathcal{A}}$ consisting of functionals of the form $F(x)=f({\langle}{\alpha}_1,x{\rangle},{\ldots},{\langle}{\alpha}_n,x{\rangle})$, where ${\langle}{\alpha},x{\rangle}$ denotes the Paley-Wiener-Zygmund stochastic integral ${\int_{0}^{T}}{\alpha}(t)dx(t)$.
Keywords
translation theorem; Gaussian process; generalized Fourier-Feynman transform; convolution product;
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