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A REPRESENTATION FOR AN INVERSE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE

. In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C a;b [0 ; T ]. The function space C a;b [0 ; T ] is induced by the generalized Brownian motion process with mean function a ( t ) and variance function b ( t ). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Z k of exponential-type functionals. We then establish that a composition of the Z k generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.