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Generalized transforms and generalized convolution products associated with Gaussian paths on function space

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  • In this paper we define a more general convolution product (associated with Gaussian processes) of functionals on the function space $ C_{a, b}[0, T] $. The function space $ C_{a, b}[0, T] $ is induced by a generalized Brownian motion process. Thus the Gaussian processes used in this paper are non-centered processes. We then develop the fundamental relationships between the generalized Fourier–Feynman transform associated with the Gaussian process and the convolution product.

    Mathematics Subject Classification: Primary: 28C20, 60G15, 60J65; Secondary: 46B09, 42B10, 46G12.


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