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Conditional first variation over Wiener paths in abstract Wiener space. (English) Zbl 1076.28013

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.

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
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