Yeh-Fourier-Feynman transforms and convolutions associated with Gaussian processes. (English) Zbl 1478.46044
Summary: In this paper, we study an analytic Yeh-Feynman integral and an analytic Yeh-Fourier-Feynman transform associated with Gaussian processes. Fubini theorems involving the generalized analytic Yeh-Feynman integrals are established. The Fubini theorems investigated in this paper are to express the iterated generalized Yeh-Feynman integrals associated with Gaussian processes as a single generalized Yeh-Feynman integral. Using our Fubini theorems, we next examined fundamental relationships (with extended versions) between generalized Yeh-Fourier-Feynman transforms and convolution products (with respect to Gaussian processes) of functionals on Yeh-Wiener space.
MSC:
| 46G12 | Measures and integration on abstract linear spaces |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 60G15 | Gaussian processes |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
Keywords:
Fubini theorem; Gaussian process; generalized Yeh-Feynman integral; generalized Yeh-Fourier-Feynman transform; convolution productReferences:
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