Acknowledgement
This study was supported by the Research Program funded by the Seoul National University of Science and Technology.
References
- R.H. Cameron and D.A. Storvick, A simple definition of the Feynman integral, with applications, Mem. Amer. Math. Soc. No. 288, Amer. Math. Soc., 1983. https://doi.org/10.1090/memo/0288
- R.H. Cameron and D.A. Storvick, Sequential Fourier-Feynman transforms, Annales Acad. Scient. Fenn. 10 (1985), 107-111.
- R.H. Cameron and D.A. Storvick, New existence theorems and evaluation formulas for sequential Feynman integrals, Proc. London Math. Soc. 52 (1986), 557-581.
- R.H. Cameron and D.A. Storvick, New existence theorems and evaluation formulas for analytic Feynman integrals, Deformations Math. Struct., Complex Analy. Phys. Appl., Kluwer Acad. Publ., Dordrecht (1989), 297-308.
- K.S. Chang, D.H. Cho, B.S. Kim, T.S. Song and I. Yoo, Relationships involving generalized Fourier-Feynman transform, convolution and first variation, Integral Transform. Spec. Funct. 16 (2005), 391-405. https://doi.org/10.1080/10652460412331320359
- K.S. Chang, D.H. Cho, B.S. Kim, T.S. Song and I. Yoo, Sequential Fourier-Feynman transform, convolution and first variation, Trans. Amer. Math. Soc. 360 (2008), 1819-1838. https://doi.org/10.1090/S0002-9947-07-04383-8
- K.S. Chang, B.S. Kim and I. Yoo, Fourier-Feynman transform, convolution and first variation of functionals on abstract Wiener space, Integral Transform. Spec. Funct. 10 (2000), 179-200. https://doi.org/10.1080/10652460008819285
- S.J. Chang and J.G. Choi, Rotation of Gaussian paths on Wiener space with applications, Banach J. Math. Anal. 12 (2018), 651-672. https://doi.org/10.1215/17358787-2017-0057
- D.M. Chung, C. Park and D. Skoug, Generalized Feynman integrals via conditional Feynman integrals, Michigan Math. J. 40 (1993), 377-391.
- T. Huffman, C. Park and D. Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), 661-673. https://doi.org/10.2307/2154908
- T. Huffman, C. Park and D. Skoug, Convolutions and Fourier-Feynman transforms of functionals involving multiple integrals, Michigan Math. J. 43 (1996), 247-261.
- T. Huffman, C. Park and D. Skoug, Generalized transforms and convolutions, Int. J. Math. Math. Sci. 20 (1997), 19-32. https://doi.org/10.1155/S0161171297000045
- C. Park and D. Skoug, A Kac-Feynman integral equation for conditional Wiener integrals, J. Integral Equations Appl. 3 (1991), 411-427. https://doi.org/10.1216/jiea/1181075633
- C. Park, D. Skoug and D. Storvick, Relationships among the first variation, the convolution product, and the Fourier-Feynman transform, Rocky Mountain J. Math. 28 (1998), 1447-1468. https://doi.org/10.1216/rmjm/1181071725
- D. Skoug and D. Storvick, A survey of results involving transforms and convolutions in function space, Rocky Mountain J. Math. 34 (2004), 1147-1176. https://doi.org/10.1216/rmjm/1181069848
- I. Yoo and B.S. Kim, Generalized sequential Feynman integral and Fourier-Feynman transform, Rocky Mountain J. Math. accepted. (2021).