Relationships among the first variation, the convolution product, and the Fourier-Feynman transform
The definitions of the \(L_p\)-Fourier-Feynman (FF) transform, convolution product and first variation for functionals over the Wiener space in the Cameron-Storvick Banach algebra \({\mathcal S}\) are briefly recalled. Relationships between these are established, expressing: (i) the FF-transform of the convolution product and the convolution product of FF-transforms; (ii) The FF-transform with respect to the first/second argument of a first variation; (iii) The first variation of a convolution product and the convolution product of two first variations with respect to their first/second arguments; (iv) The FF-transforms of (iii); (v) The first variations of (i).
scientific article; zbMATH DE number 1309887
scientific article