Relationships among transforms, convolutions, and first variations
In this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionals F on Wiener space of the form F(x)=f(〈α1,x〉,…,〈αn,x〉), (*) where 〈αj,x〉 denotes...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299221916 |
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| _version_ | 1832554900559495168 |
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| author | Jeong Gyoo Kim Jung Won Ko Chull Park David Skoug |
| author_facet | Jeong Gyoo Kim Jung Won Ko Chull Park David Skoug |
| author_sort | Jeong Gyoo Kim |
| collection | DOAJ |
| description | In this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionals F on Wiener space of the form F(x)=f(〈α1,x〉,…,〈αn,x〉), (*) where 〈αj,x〉 denotes the Paley-Wiener-Zygmund stochastic integral ∫0Tαj(t)dx(t). |
| format | Article |
| id | doaj-art-3a702cff0bf345f68520cb608d3e9ed8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3a702cff0bf345f68520cb608d3e9ed82025-02-03T05:50:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122119120410.1155/S0161171299221916Relationships among transforms, convolutions, and first variationsJeong Gyoo Kim0Jung Won Ko1Chull Park2David Skoug3Department of Mathematics, Yonsei University, Seoul 120-749, KoreaDepartment of Mathematics, Yonsei University, Seoul 120-749, KoreaDepartment of Mathematics and Statistics, Miami University, Oxford, OH 45056, USADepartment of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588, USAIn this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionals F on Wiener space of the form F(x)=f(〈α1,x〉,…,〈αn,x〉), (*) where 〈αj,x〉 denotes the Paley-Wiener-Zygmund stochastic integral ∫0Tαj(t)dx(t).http://dx.doi.org/10.1155/S0161171299221916Fourier-Feynman transformconvolution productfirst variationFeynman integral. |
| spellingShingle | Jeong Gyoo Kim Jung Won Ko Chull Park David Skoug Relationships among transforms, convolutions, and first variations International Journal of Mathematics and Mathematical Sciences Fourier-Feynman transform convolution product first variation Feynman integral. |
| title | Relationships among transforms, convolutions, and first variations |
| title_full | Relationships among transforms, convolutions, and first variations |
| title_fullStr | Relationships among transforms, convolutions, and first variations |
| title_full_unstemmed | Relationships among transforms, convolutions, and first variations |
| title_short | Relationships among transforms, convolutions, and first variations |
| title_sort | relationships among transforms convolutions and first variations |
| topic | Fourier-Feynman transform convolution product first variation Feynman integral. |
| url | http://dx.doi.org/10.1155/S0161171299221916 |
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