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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Sequential Fourier-Feynman transform, convolution and first variation


Authors: K. S. Chang, D. H. Cho, B. S. Kim, T. S. Song and I. Yoo
Journal: Trans. Amer. Math. Soc. 360 (2008), 1819-1838
MSC (2000): Primary 28C20, 44A20
Published electronically: November 19, 2007
MathSciNet review: 2366964
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-07-04383-8
Keywords: Sequential Feynman integral, sequential Fourier-Feynman transform, convolution, translation theorem, Parseval's relation
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.