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

Seung Jun Chang; Jae Gil Choi; David Skoug

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arXiv · 1511.03564

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

Seung Jun Chang·Jae Gil Choi·David Skoug

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Abstract

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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BibTeX RIS

Seung Jun Chang, Jae Gil Choi, David Skoug. 2019-04-17. Algebraic structure of the $L_2$ analytic Fourier-Feynman transform associated with Gaussian processes on Wiener space. https://arxiv.org/abs/1511.03564

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