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Generalized sequential convolution product for the generalized sequential Fourier-Feynman transform

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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)

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  10. T. Huffman, "Analytic Fourier-Feynman transforms and convolution", Trans. Amer. Math. Soc, 347, pp.661~673 (1995)
  11. T. Huffman, "Convolutions and Fourier-Feynman transforms of function-als involving multiple integrals", Michigan Math. J, 43, pp.247~261 (1996)
  12. T. Huffman, "Generalized transforms and convolutions", Int. J. Math. Math. Sci, 20, pp.19~32 (1997)
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  16. I. Yoo, "Generalized sequential Feynman integral and Fourier-Feynman transform", Rocky Mountain J. Math (2021)

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