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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202006361 |
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| _version_ | 1832550181860540416 |
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| author | Seung Jun Chang Jae Gil Choi |
| author_facet | Seung Jun Chang Jae Gil Choi |
| author_sort | Seung Jun Chang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-01704839f505455a916d8ebc86ed5739 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-01704839f505455a916d8ebc86ed57392025-02-03T06:07:21ZengWileyInternational 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/S0161171202006361 |
| work_keys_str_mv | AT seungjunchang relationshipsofconvolutionproductsgeneralizedtransformsandthefirstvariationonfunctionspace AT jaegilchoi relationshipsofconvolutionproductsgeneralizedtransformsandthefirstvariationonfunctionspace |