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Zbl 0901.28010
Huffman, Timothy; Park, Chull; Skoug, David
Convolution and Fourier-Feynman transforms. (English)
[J] Rocky Mt. J. Math. 27, No.3, 827-841 (1997). ISSN 0035-7596

For a class of functionals on the Wiener space of the form $$F(x)= \exp\Biggl\{\int^T_0 f(t,x(t))dt\Biggr\},$$ a new definition of the convolution product is proposed. This convolution product is commutative. The $L_p$ analytic Fourier-Feynman transform, introduced by {\it G. W. Johnson} and {\it D. L. Skoug} [Mich. Math. J. 26, 103-127 (1979; Zbl 0409.28007)], is applied. It is shown that the transform of the convolution product is a product of the transforms.\par In general the convolution product is not associative. The list of cases is given when the associativity does hold.
[Oleksandr Kukush (Kyiv)]

MSC 2000:: *28C20 Set functions and measures and integrals in infinite-dim. spaces

Keywords: Wiener space; convolution product; Fourier-Feynman transform; associativity

Citations: Zbl 0409.28007

Cited in: Zbl 1001.28007 Zbl 1015.28016

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