Generalized Integral Transforms via the Series Expressions
From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/539 |
| _version_ | 1797571334201409536 |
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| author | Hyun Soo Chung |
| author_facet | Hyun Soo Chung |
| author_sort | Hyun Soo Chung |
| collection | DOAJ |
| description | From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods. |
| first_indexed | 2024-03-10T20:38:53Z |
| format | Article |
| id | doaj.art-8030f634979946f19ac11759fedf51a7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:38:53Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8030f634979946f19ac11759fedf51a72023-11-19T20:50:01ZengMDPI AGMathematics2227-73902020-04-018453910.3390/math8040539Generalized Integral Transforms via the Series ExpressionsHyun Soo Chung0Department of Mathematics, Dankook University, Cheonan 31116, KoreaFrom the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods.https://www.mdpi.com/2227-7390/8/4/539generalized integral transformkernelWiener-Itô-Chaos expansionRiesz’s theoremHahn-Banach theorem |
| spellingShingle | Hyun Soo Chung Generalized Integral Transforms via the Series Expressions Mathematics generalized integral transform kernel Wiener-Itô-Chaos expansion Riesz’s theorem Hahn-Banach theorem |
| title | Generalized Integral Transforms via the Series Expressions |
| title_full | Generalized Integral Transforms via the Series Expressions |
| title_fullStr | Generalized Integral Transforms via the Series Expressions |
| title_full_unstemmed | Generalized Integral Transforms via the Series Expressions |
| title_short | Generalized Integral Transforms via the Series Expressions |
| title_sort | generalized integral transforms via the series expressions |
| topic | generalized integral transform kernel Wiener-Itô-Chaos expansion Riesz’s theorem Hahn-Banach theorem |
| url | https://www.mdpi.com/2227-7390/8/4/539 |
| work_keys_str_mv | AT hyunsoochung generalizedintegraltransformsviatheseriesexpressions |