Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function
We investigate the behavior of the unbounded cylinder function Fx=∫0Tα1tdxt2k⋅∫0Tα2tdxt2k⋅⋯⋅∫0Tαntdxt2k, k=1,2,… whose analytic Wiener integral and analytic Feynman integral exist, we prove some relationships among the analytic Wiener integral, the analytic Feynman integral, and the Wiener integral,...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2671474 |
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| _version_ | 1850160295464402944 |
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| author | Kim Young Sik |
| author_facet | Kim Young Sik |
| author_sort | Kim Young Sik |
| collection | DOAJ |
| description | We investigate the behavior of the unbounded cylinder function Fx=∫0Tα1tdxt2k⋅∫0Tα2tdxt2k⋅⋯⋅∫0Tαntdxt2k, k=1,2,… whose analytic Wiener integral and analytic Feynman integral exist, we prove some relationships among the analytic Wiener integral, the analytic Feynman integral, and the Wiener integral, and we prove a change of scale formula for the Wiener integral about the unbounded function on the Wiener space C00,T. |
| format | Article |
| id | doaj-art-b6c2d50895844e0f9996bb4b508676a6 |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b6c2d50895844e0f9996bb4b508676a62025-08-20T02:23:11ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/26714742671474Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder FunctionKim Young Sik0Department of Mathematics, College of Natural Sciences, Industry-University Cooperation Foundation, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of KoreaWe investigate the behavior of the unbounded cylinder function Fx=∫0Tα1tdxt2k⋅∫0Tα2tdxt2k⋅⋯⋅∫0Tαntdxt2k, k=1,2,… whose analytic Wiener integral and analytic Feynman integral exist, we prove some relationships among the analytic Wiener integral, the analytic Feynman integral, and the Wiener integral, and we prove a change of scale formula for the Wiener integral about the unbounded function on the Wiener space C00,T.http://dx.doi.org/10.1155/2020/2671474 |
| spellingShingle | Kim Young Sik Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function Complexity |
| title | Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function |
| title_full | Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function |
| title_fullStr | Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function |
| title_full_unstemmed | Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function |
| title_short | Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function |
| title_sort | analytic feynman integral and a change of scale formula for wiener integrals of an unbounded cylinder function |
| url | http://dx.doi.org/10.1155/2020/2671474 |
| work_keys_str_mv | AT kimyoungsik analyticfeynmanintegralandachangeofscaleformulaforwienerintegralsofanunboundedcylinderfunction |