Generalized sequential convolution product for the generalized sequential Fourier-Feynman transform
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초록
This paper is a further development of the recent results by the authors on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra $\hat{\mathcal S}$ and some related functionals. We investigate various relationships between the generalized sequential Fourier-Feynman transform and the generalized sequential convolution product of functionals. Parseval's relation for the generalized sequential Fourier-Feynman transform is also given.
Abstract
This paper is a further development of the recent results by the authors on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra $\hat{\mathcal S}$ and some related functionals. We investigate various relationships between the generalized sequential Fourier-Feynman transform and the generalized sequential convolution product of functionals. Parseval's relation for the generalized sequential Fourier-Feynman transform is also given.
참고문헌 (16)
- R. H. Cameron, "A simple definition of the Feynman integral, with applications", Mem. Amer. Math. Soc, (288) (1983)
- R. H. Cameron, "Sequential Fourier-Feynman transforms", Annales Acad. Sci-ent. Fenn, 10, pp.107~111 (1985)
- R. H. Cameron, "New existence theorems and evaluation formulas for sequential Feynman integrals", Proc. London Math. Soc, 52, pp.557~581 (1986)
- R.H. Cameron, "New existence theorems and evaluation formulas for analytic Feynman integrals", Deformations Math. Struct., Complex Analy. Phys. Appl., Kluwer Acad. Publ., Dordrecht, pp.297~308 (1989)
- K. S. Chang, "Relationships involving generalized Fourier-Feynman transform, convolution and first variation", Integral Transform. Spec. Funct, 16, pp.391~405 (2005)
- K. S. Chang, "Sequential Fourier-Feynman transform, convolution and first variation", Trans. Amer. Math. Soc, 360, pp.1819~1838 (2008)
- K. S. Chang, "convolution and first variation of functionals on abstract Wiener space", Integral Transform. Spec. Funct, 10, pp.179~200 (2000)
- S. J. Chang, "Rotation of Gaussian paths on Wiener space with applications", Ba-nach J. Math. Anal, 12, pp.651~672 (2018)
- D. M. Chung, "Generalized Feynman integrals via conditional Feynman integrals", Michigan Math. J, 40, pp.377~391 (1993)
- T. Huffman, "Analytic Fourier-Feynman transforms and convolution", Trans. Amer. Math. Soc, 347, pp.661~673 (1995)
- T. Huffman, "Convolutions and Fourier-Feynman transforms of function-als involving multiple integrals", Michigan Math. J, 43, pp.247~261 (1996)
- T. Huffman, "Generalized transforms and convolutions", Int. J. Math. Math. Sci, 20, pp.19~32 (1997)
- C. Park, "A Kac-Feynman integral equation for conditional Wiener integrals", J. Integral Equations Appl, 3, pp.411~427 (1991)
- C. Park, "Relationships among the first variation, the convolution product, and the Fourier-Feynman transform", Rocky Mountain J. Math, 28, pp.1447~1468 (1998)
- D. Skoug, "A survey of results involving transforms and convolutions in function space", Rocky Mountain J. Math, 34, pp.1147~1176 (2004)
- I. Yoo, "Generalized sequential Feynman integral and Fourier-Feynman transform", Rocky Mountain J. Math (2021)
