Relationships of convolution products, generalized transforms, and the first variation on function space

We use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. We then examine the various relationships that exist among the first variation, the generalized Fourier-Feynman transform, and the convolution product f...

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Main Authors:	Seung Jun Chang, Jae Gil Choi
Format:	Article
Language:	English
Published:	Hindawi Limited 2002-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/S0161171202006361

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record_format	Article
spelling	doaj-01704839f505455a916d8ebc86ed57392020-11-25T01:24:59ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01291059160810.1155/S0161171202006361Relationships of convolution products, generalized transforms, and the first variation on function spaceSeung Jun Chang0Jae Gil Choi1Department of Mathematics, Dankook University, Cheonan 330-714, South KoreaDepartment of Mathematics, Dankook University, Cheonan 330-714, South KoreaWe use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. We then examine the various relationships that exist among the first variation, the generalized Fourier-Feynman transform, and the convolution product for functionals on function space that belong to a Banach algebra S(Lab[0,T]). These results subsume similar known results obtained by Park, Skoug, and Storvick (1998) for the standard Wiener process.http://dx.doi.org/10.1155/S0161171202006361
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Seung Jun Chang Jae Gil Choi
spellingShingle	Seung Jun Chang Jae Gil Choi Relationships of convolution products, generalized transforms, and the first variation on function space International Journal of Mathematics and Mathematical Sciences
author_facet	Seung Jun Chang Jae Gil Choi
author_sort	Seung Jun Chang
title	Relationships of convolution products, generalized transforms, and the first variation on function space
title_short	Relationships of convolution products, generalized transforms, and the first variation on function space
title_full	Relationships of convolution products, generalized transforms, and the first variation on function space
title_fullStr	Relationships of convolution products, generalized transforms, and the first variation on function space
title_full_unstemmed	Relationships of convolution products, generalized transforms, and the first variation on function space
title_sort	relationships of convolution products, generalized transforms, and the first variation on function space
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2002-01-01
description	We use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. We then examine the various relationships that exist among the first variation, the generalized Fourier-Feynman transform, and the convolution product for functionals on function space that belong to a Banach algebra S(Lab[0,T]). These results subsume similar known results obtained by Park, Skoug, and Storvick (1998) for the standard Wiener process.
url	http://dx.doi.org/10.1155/S0161171202006361
work_keys_str_mv	AT seungjunchang relationshipsofconvolutionproductsgeneralizedtransformsandthefirstvariationonfunctionspace AT jaegilchoi relationshipsofconvolutionproductsgeneralizedtransformsandthefirstvariationonfunctionspace
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Relationships of convolution products, generalized transforms, and the first variation on function space

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