Generalized first variation and generalized sequential Fourier-Feynman transform
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra $\hat{\mathcal S}$ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.
Abstract
This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra $\hat{\mathcal S}$ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.
참고문헌 (17)
- J.M. Ahn, "Fourier-Feynman transform, convolution and first variation", Acta Math. Hungar, 100, pp.215~235 (2003)
- R. H. Cameron, "Analytic functions" (1980), Springer
- R. H. Cameron, "A simple definition of the Feynman integral, with applications", Mem. Amer. Math. Soc, 288 (1983), Amer. Math. Soc
- R. H. Cameron, "Sequential Fourier-Feynman transforms", Annales Acad. Scient. 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, 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, "Fourier-Feynman transform, convolution and first variation of functionals on abstract Wiener space", Integral Transform. Spec. Funct, 10, pp.179~200 (2000)
- S. J. Chang, "Analytic Fourier-Feynman transforms and convolution products associated with Gaussian processes on Wiener space", Banach J. Math. Anal, 11, pp.785~807 (2017)
- 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 functionals involving multiple integrals", Michigan Math. J, 43, pp.247~261 (1996)
- 김병수, "Generalized sequential convolution product for the generalized sequential Fourier-Feynman transform", 한국수학논문집, 29(2), pp.321~332 (2021), 강원경기수학회
- 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 Fourier-Feynman transform", Rocky Mountain J. Math, 51, pp.2251~2268 (2021)
