Relationships among the first variation, the convolution product, and the Fourier-Feynman transform
type: Item
instance of: scholarly article
title: Relationships among the first variation, the convolution product, and the Fourier-Feynman transform
zbMATH Open document ID: 0934.28008
author: David Storvick
author: Chull Park
author: David Skoug
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-06-28T00:00:00Z
full work available at URL: CONT28-4.html
review text: 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).
reviewed by: Nicolae Angelescu
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 81S40
zbMATH DE Number: 1309887
zbMATH Keywords: Fourier-Feynman transform
zbMATH Keywords: convolution product
zbMATH Keywords: first variation
zbMATH Keywords: Wiener space
MaRDI profile type: Publication
OpenAlex ID: W1981754482
cites work: The First Variation of an Indefinite Wiener Integral
cites work: An \(L_2\) analytic Fourier-Feynman transform
cites work: Q3881077
cites work: Q4764535
cites work: Q3039630
cites work: The Feynman integral of quadratic potentials depending on two time variables
cites work: Q3141228
cites work: Analytic Fourier-Feynman Transforms and Convolution
cites work: Convolution and Fourier-Feynman transforms
cites work: Convolutions and Fourier-Feynman transforms of functionals involving multiple integrals
cites work: An \(L_p\) analytic Fourier-Feynman transform
cites work: Scale-invariant measurability in Wiener space
cites work: Notes on the Feynman integral. II
cites work: The Feynman integral of quadratic potentials depending on n time variables
cites work: Convolution in Fourier-Wiener transform
cites work: Convolution and the Fourier-Wiener transform on abstract Wiener space
DOI: 10.1216/RMJM/1181071725
description: scientific article; zbMATH DE number 1309887