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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A change of scale formula for a function space integral on $ C_{a,b}[0,T]$


Authors: Il Yoo, Bong Jin Kim and Byoung Soo Kim
Journal: Proc. Amer. Math. Soc. 141 (2013), 2729-2739
MSC (2000): Primary 28C20; Secondary 60J25, 60J65
Published electronically: April 5, 2013
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11598-4
PII: S 0002-9939(2013)11598-4
Keywords: Change of scale formula, function space integral, generalized analytic Feynman integral
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.