Conditional Fourier-Feynman Transforms with Drift on a Function Space
In this paper we derive change of scale formulas for conditional analytic Fourier-Feynman transforms and conditional convolution products of the functions which are the products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transfor...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/9483724 |
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| _version_ | 1832560858002096128 |
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| author | Dong Hyun Cho Suk Bong Park |
| author_facet | Dong Hyun Cho Suk Bong Park |
| author_sort | Dong Hyun Cho |
| collection | DOAJ |
| description | In this paper we derive change of scale formulas for conditional analytic Fourier-Feynman transforms and conditional convolution products of the functions which are the products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the complex Borel measures on L2[0,T] using two simple formulas for conditional expectations with a drift on an analogue of Wiener space. Then we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we establish various changes of scale formulas for the conditional transforms and the conditional convolution products. |
| format | Article |
| id | doaj-art-354077301017424085d641e7ca7d5dd9 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-354077301017424085d641e7ca7d5dd92025-02-03T01:26:26ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/94837249483724Conditional Fourier-Feynman Transforms with Drift on a Function SpaceDong Hyun Cho0Suk Bong Park1Department of Mathematics, Kyonggi University, Suwon 16227, Republic of KoreaDepartment of Mathematics, Korea Military Academy, PO Box 77-1, Seoul, Republic of KoreaIn this paper we derive change of scale formulas for conditional analytic Fourier-Feynman transforms and conditional convolution products of the functions which are the products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the complex Borel measures on L2[0,T] using two simple formulas for conditional expectations with a drift on an analogue of Wiener space. Then we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we establish various changes of scale formulas for the conditional transforms and the conditional convolution products.http://dx.doi.org/10.1155/2019/9483724 |
| spellingShingle | Dong Hyun Cho Suk Bong Park Conditional Fourier-Feynman Transforms with Drift on a Function Space Journal of Function Spaces |
| title | Conditional Fourier-Feynman Transforms with Drift on a Function Space |
| title_full | Conditional Fourier-Feynman Transforms with Drift on a Function Space |
| title_fullStr | Conditional Fourier-Feynman Transforms with Drift on a Function Space |
| title_full_unstemmed | Conditional Fourier-Feynman Transforms with Drift on a Function Space |
| title_short | Conditional Fourier-Feynman Transforms with Drift on a Function Space |
| title_sort | conditional fourier feynman transforms with drift on a function space |
| url | http://dx.doi.org/10.1155/2019/9483724 |
| work_keys_str_mv | AT donghyuncho conditionalfourierfeynmantransformswithdriftonafunctionspace AT sukbongpark conditionalfourierfeynmantransformswithdriftonafunctionspace |