Algebraic aspects of the $L_2$ analytic Gaussian--Fourier--Feynman transform via Gaussian processes on Wiener space

In this research, we investigate several rotation properties of the generalized Wiener integral with respect to Gaussian processes, which are then used to analyze an $L_2$ analytic Gaussian--Fourier--Feynman transform. Our results indicate that the $L_2$ analytic Gaussian--Fourier--Feynman transforms are linear operator isomorphisms from a Hilbert space into itself. We then proceed to investigate the algebraic structure of these generalized transforms and establish that two classes of the generalized transforms on Wiener space are group isomorphic.