Fourier-Feynman transforms for functionals in a generalized Fresnel class
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Abstract
Hu??man, Park and Skoug introduced various results for the Lp analytic Fourier-Feynman transform and the convolution for func- tionals on classical Wiener space which belong to some Banach algebra S introduced by Cameron and Storvick. Also Chang, Kim and Yoo ex- tended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class FA1;A2 containing F(B). In this paper, we establish various interesting relationships and expres- sions involving the ¯rst variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in FA1;A2 .
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