A change of scale formula for a function space integral on $C_{a,b}[0,T]$
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- by Il Yoo, Bong Jin Kim and Byoung Soo Kim PDF
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Abstract:
Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in a Banach algebra ${\mathcal S}$ on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class ${\mathcal F}(B)$ and in a generalized Fresnel class ${\mathcal F}_{A_1,A_2}$ on abstract Wiener space. We establish a relationship between a function space integral and a generalized analytic Feynman integral on $C_{a,b}[0,T]$ for functionals in a Banach algebra ${\mathcal S}(L_{a,b}^2[0,T])$. Moreover, we obtain a change of scale formula for a function space integral on $C_{a,b}[0,T]$ of these functionals.References
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Additional Information
- Il Yoo
- Affiliation: Department of Mathematics, Yonsei University, Wonju 220-710, Republic of Korea
- Email: iyoo@yonsei.ac.kr
- Bong Jin Kim
- Affiliation: Department of Mathematics, Daejin University, Pocheon 487-711, Republic of Korea
- Email: bjkim@daejin.ac.kr
- Byoung Soo Kim
- Affiliation: School of Liberal Arts, Seoul National University of Science and Technology, Seoul 139-743, Republic of Korea
- Email: mathkbs@seoultech.ac.kr
- Received by editor(s): January 4, 2011
- Received by editor(s) in revised form: October 28, 2011
- Published electronically: April 5, 2013
- Additional Notes: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0022563)
- Communicated by: Marius Junge
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2729-2739
- MSC (2000): Primary 28C20; Secondary 60J25, 60J65
- DOI: https://doi.org/10.1090/S0002-9939-2013-11598-4
- MathSciNet review: 3056563