Convolution and Fourier-Feynman transforms
type: Item
instance of: scholarly article
title: Convolution and Fourier-Feynman transforms
zbMATH Open document ID: 0901.28010
author: Timothy Huffman
author: Chull Park
author: David Skoug
published in: Rocky Mountain Journal of Mathematics
publication date: 1998-04-20T00:00:00Z
full work available at URL: CONT27-3.html
review text: 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 \textit{G. W. Johnson} and \textit{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. In general the convolution product is not associative. The list of cases is given when the associativity does hold.
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 1143471
zbMATH Keywords: Wiener space
zbMATH Keywords: convolution product
zbMATH Keywords: Fourier-Feynman transform
zbMATH Keywords: associativity
reviewed by: A. Kukush
MaRDI profile type: Publication
OpenAlex ID: W2053494920
cites work: Q5579941
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cites work: Q5640160
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DOI: 10.1216/RMJM/1181071896
description: scientific article; zbMATH DE number 1143471