Conditional Fourier-Feynman transforms of variations over Wiener paths in abstract Wiener space

Abstract

Wiener spaces via several papers [1, 2, 3, 8, 17]. In par-ticular, using a recurrence relation, Chang, Song and Yo derived theFourier-Feynman transform for the product of a function in the Fresnelclass, withn linear factors ([8]).On the other hand, in [19], Yo introduced a Banach algebraS00Bwhich corresponds to the Banach algebraS00introduced by Cameronand Storvick in [4]. In [6], Chang, Cho and Yo introduced a conceptof conditional analytic Feynman integral over Wiener paths in abstractWiener space and in [7], they evaluated the integrals for the functions inthe Banach algebraS00B. In [5], Chang, Cho, Kim, Song and Yo intro-duced a kind of conditional Fourier-Feynman transform and in [9], ChoReceived February 1, 2005. Revised May 12, 2005.2000 Mathematics Subject Classication: 28C20.Key words and phrases: conditional Feynman integral, conditional rst variation,conditional Fourier-Feynman transform, conditional Wiener integral, Feynman inte-gral, rst variation, Fourier-Feynman transform, Wiener integral, Wiener paths in