Integration by parts formulas involving generalized Fourier-Feynman transforms on function space. (English) Zbl 1014.60077
Summary: In an upcoming paper, S. J. Chang and D. L. Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we establish several integration by parts formulas involving generalized Feynman integrals, generalized Fourier-Feynman transforms, and the first variation of functionals of the form \(F(x)=f(\langle{\alpha_{1} , x}\rangle, \dots , \langle{\alpha_{n} , x}\rangle)\) where \(\langle{\alpha ,x}\rangle\) denotes the Paley-Wiener-Zygmund stochastic integral \(\int_{0}^{T} \alpha(t) dx(t)\).
MSC:
| 60J65 | Brownian motion |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
Keywords:
generalized Brownian motion process; generalized analytic Feynman integral; generalized analytic Fourier-Feynman transform; first variation; Cameron-Storvick type theoremReferences:
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