Algebraic structure of the L₂ analytic Fourier-Feynman transform associated with Gaussian processes on Wiener space

2015/11/09 by Chang, Seung Jun, Choi, Jae Gil, Skoug, David
#28C20 #54H15 #60G15 #60J25 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1511.03564

Abstract

In this paper we study algebraic structures of the classes of the L₂ 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 L₂ analytic Fourier-Feynman transforms associated with Gaussian processes. Our results show that these L₂ 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.

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