Cho, Dong Hyun Conditional first variation over Wiener paths in abstract Wiener space. (English) Zbl 1076.28013 J. Korean Math. Soc. 42, No. 5, 1031-1056 (2005). Summary: In this paper, we define the conditional first variation over Wiener paths in an abstract Wiener space and investigate its properties. Using these properties, we also investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transforms of functions in a Banach algebra which is equivalent to the Fresnel class. Finally, we provide another method evaluating the Fourier-Feynman transform for the product of a function in the Banach algebra with \(n\) linear factors. Cited in 1 ReviewCited in 1 Document MSC: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) 46J10 Banach algebras of continuous functions, function algebras Keywords:conditional first variation; conditional Fourier-Feynman transform; Fresnel class; Wiener paths; abstract Wiener space; Banach algebra PDFBibTeX XMLCite \textit{D. H. Cho}, J. Korean Math. Soc. 42, No. 5, 1031--1056 (2005; Zbl 1076.28013) Full Text: DOI