Abstract
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.
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The author would like to express his gratitude to the editor and the referees for their valuable comments and suggestions which have improved the original paper.
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Communicated by Constantin Niculescu.
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Choi, J.G. Yeh–Fourier–Feynman transforms and convolutions associated with Gaussian processes. Ann. Funct. Anal. 12, 41 (2021). https://doi.org/10.1007/s43034-021-00128-7
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DOI: https://doi.org/10.1007/s43034-021-00128-7
Keywords
- Fubini theorem
- Gaussian process
- Generalized Yeh–Feynman integral
- Generalized Yeh–Fourier–Feynman transform
- Convolution product