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Zbl 0934.28008
Park, Chull; Skoug, David; Storvick, David
Relationships among the first variation, the convolution product, and the Fourier-Feynman transform.
(English)
[J] Rocky Mt. J. Math. 28, No.4, 1447-1468 (1998). ISSN 0035-7596

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 ${\cal S}$ 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).
[N.Angelescu (Bucureşti)]
MSC 2000:
*28C20 Set functions and measures and integrals in infinite-dim. spaces
44A15 Special transforms
81S40 Path integrals in quantum mechanics

Keywords: Fourier-Feynman transform; convolution product; first variation; Wiener space

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