Generalized Fourier-Feynman transform and sequential transforms on function space
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In this paper we rst investigate the existence of the gener-alized Fourier-Feynman transform of the functional F given by F(x) = ^((e1; x)~,..., (en, x)~);where (e, x) denotes the Paley-Wiener-Zygmund stochastic integral with x in a very general function space Ca;b[0; T] and ^ is the Fourier transform of complex measure on B(Rn) with nite total variation. We then de ne two sequential transforms. Finally, we establish that the one is to identify the generalized Fourier-Feynman transform and the another transform acts like an inverse generalized Fourier-Feynman transform.
Abstract
In this paper we rst investigate the existence of the gener-alized Fourier-Feynman transform of the functional F given by F(x) = ^((e1; x)~,..., (en, x)~);where (e, x) denotes the Paley-Wiener-Zygmund stochastic integral with x in a very general function space Ca;b[0; T] and ^ is the Fourier transform of complex measure on B(Rn) with nite total variation. We then de ne two sequential transforms. Finally, we establish that the one is to identify the generalized Fourier-Feynman transform and the another transform acts like an inverse generalized Fourier-Feynman transform.
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