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Generalized first variation and generalized sequential Fourier-Feynman transform

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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)

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  11. D. M. Chung, "Generalized Feynman integrals via conditional Feynman integrals", Michigan Math. J, 40, pp.377~391 (1993)
  12. T. Huffman, "Analytic Fourier-Feynman transforms and convolution", Trans. Amer. Math. Soc, 347, pp.661~673 (1995)
  13. T. Huffman, "Convolutions and Fourier-Feynman transforms of functionals involving multiple integrals", Michigan Math. J, 43, pp.247~261 (1996)
  14. 김병수, "Generalized sequential convolution product for the generalized sequential Fourier-Feynman transform", 한국수학논문집, 29(2), pp.321~332 (2021), 강원경기수학회
  15. C. Park, "Relationships among the first variation, the convolution product, and the Fourier-Feynman transform", Rocky Mountain J. Math, 28, pp.1447~1468 (1998)
  16. D. Skoug, "A survey of results involving transforms and convolutions in function space", Rocky Mountain J. Math, 34, pp.1147~1176 (2004)
  17. I. Yoo, "Generalized sequential Fourier-Feynman transform", Rocky Mountain J. Math, 51, pp.2251~2268 (2021)

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