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Algebraic structure of the analytic Fourier-Feynman transform associated with Gaussian processes on Wiener space
In this paper we study algebraic structures of the classes of the
analytic Fourier-Feynman transforms on Wiener space. To do this we first
develop several rotation properties of the generalized Wiener integral
associated with Gaussian processes. We then proceed to analyze the
analytic Fourier-Feynman transforms associated with Gaussian processes. Our
results show that these analytic Fourier--Feynman transforms are actually
linear operator isomorphisms from a Hilbert space into itself. We finally
investigate the algebraic structures of these classes of the transforms on
Wiener space, and show that they indeed are group isomorphic.Comment: 19page