Algebraic structure of the L_2 analytic Fourier-Feynman transform associated with Gaussian processes on Wiener space release_z5oxtjl2nzco3ccnp3eyebwcaq

by Seung Jun Chang, Jae Gil Choi, David Skoug

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In this paper we study algebraic structures of the classes of the L_2 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 L_2 analytic Fourier-Feynman transforms associated with Gaussian processes. Our results show that these L_2 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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Date   2019-04-17
Version   v2
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arXiv  1511.03564v2
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