Analytic Fourier-Feynman transform and first variation on abstract Wiener space. (Q2718444)

An \(L_p\)-analytic Fourier-Feynman transform for functionals on a Wiener space was developed by Brue, Cameron and Storvick, and Johnson and Skoug. Huffman, Park and Skoug defined a convoluton product for functionals on the Wiener space and they showed that the analytic Fourier-Feynman transform of the convolution product is the product of transforms.NEWLINENEWLINE Cameron obtained the Wiener integral of first variation of the functional in terms of the Wiener integral of the product with a linear factor. Chang, Kim and Yoo established the relationships among Fourier-Feynman transform, first variation and convolution product on the abstract Wiener space.NEWLINENEWLINE In this paper, the authors express the analytic Feynman integral of the first variation of a functional in terms of an analytic Feynman integral of the product of the functional with a linear factor and obtain an integration by parts formula for the analytic Feynman integral of functionals on the abstract Wiener space.