Sequential Fourier-Feynman transform, convolution and first variation
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- by K. S. Chang, D. H. Cho, B. S. Kim, T. S. Song and I. Yoo PDF
- Trans. Amer. Math. Soc. 360 (2008), 1819-1838 Request permission
Abstract:
Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra $\hat {\mathcal S}$ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or continuous. Also we study the relationships involving this transform and the first variation.References
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Additional Information
- K. S. Chang
- Affiliation: Department of Mathematics, Yonsei University, Seoul 120-749, Korea
- Email: kunchang@yonsei.ac.kr
- D. H. Cho
- Affiliation: Department of Mathematics, Kyonggi University, Suwon 443-760, Korea
- Email: j94385@kyonggi.ac.kr
- B. S. Kim
- Affiliation: School of Liberal Arts, Seoul National University of Technology, Seoul 139-743, Korea
- Email: mathkbs@snut.ac.kr
- T. S. Song
- Affiliation: Department of Computer Engineering, Mokwon University, Daejeon 302-729, Korea
- Email: teukseob@mokwon.ac.kr
- I. Yoo
- Affiliation: Department of Mathematics, Yonsei University, Wonju 220-710, Korea
- Email: iyoo@yonsei.ac.kr
- Received by editor(s): October 5, 2005
- Published electronically: November 19, 2007
- Additional Notes: This research was supported by the Basic Science Research Institute Program, Korea Research Foundation under Grant KRF 2003-005-C00011. The third author was supported by the research fund of Seoul National University of Technology
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 1819-1838
- MSC (2000): Primary 28C20, 44A20
- DOI: https://doi.org/10.1090/S0002-9947-07-04383-8
- MathSciNet review: 2366964