대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권1호
  • /
  • Pages.217-231
  • /
  • 2013
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRAL ON FUNCTION SPACE

  • 투고 : 2011.07.21
  • 발행 : 2013.01.31
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초록

In this paper we establish a Fubini theorem for generalized analytic Feynman integral and $L_1$ generalized analytic Fourier-Feynman transform for the functional of the form $$F(x)=f({\langle}{\alpha}_1,\;x{\rangle},\;{\cdots},\;{\langle}{{\alpha}_m,\;x{\rangle}),$$ where {${\alpha}_1$, ${\cdots}$, ${\alpha}_m$} is an orthonormal set of functions from $L_{a,b}^2[0,T]$. We then obtain several generalized analytic Feynman integration formulas involving generalized analytic Fourier-Feynman transforms.

키워드

참고문헌

  1. M. D. Brue, A functional transform for Feynman integrals similar to the Fourier transform, Thesis, Univ. of Minnesota, Minneapolis, 1972.
  2. R. H. Cameron and D. A. Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), no. 1, 1-30. https://doi.org/10.1307/mmj/1029001617
  3. S. J. Chang and D. M. Chung, Conditional function space integrals with applications, Rocky Mountain J. Math. 26 (1996), no. 1, 37-62. https://doi.org/10.1216/rmjm/1181072102
  4. S. J. Chang, J. G. Choi, and D. Skoug, Integration by parts formulas involving generalized Fourier-Feynman transforms on function space, Trans. Amer. Math. Soc. 355 (2003), no. 7, 2925-2948. https://doi.org/10.1090/S0002-9947-03-03256-2
  5. S. J. Chang and I. Y. Lee, A Fubini theorem for generalized analytic Feynman integrals and Fourier-Feynman transforms on function space, Bull. Korean Math. Soc. 40 (2003), no. 3, 437-456. https://doi.org/10.4134/BKMS.2003.40.3.437
  6. D. M. Chung, Scale-invariant measurability in abstract Wiener spaces, Pacific J. Math. 130 (1987), no. 1, 27-40. https://doi.org/10.2140/pjm.1987.130.27
  7. T. Huffman, D. Skoug, and D. Storvick, A Fubini theorem for analytic Feynman integrals with applications, J. Korean Math. Soc. 38 (2001), no. 2, 409-420.
  8. T. Huffman, Integration formulas involving Fourier-Feynman transforms via a Fubini theorem, J. Korean Math. Soc. 38 (2001), no. 2, 421-435.
  9. G. W. Johnson and D. L. Skoug, An $L_p$ analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), no. 1, 103-127. https://doi.org/10.1307/mmj/1029002166
  10. G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), no. 1, 157-176. https://doi.org/10.2140/pjm.1979.83.157
  11. E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967.
  12. J. Yeh, Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments, Illinois J. Math. 15 (1971), 37-46.
  13. J. Yeh, Stochastic Processes and the Wiener Integral, Marcel Dekker, Inc., New York, 1973.

피인용 문헌

  1. generalized analytic Fourier–Feynman transform vol.29, pp.9, 2018, https://doi.org/10.1080/10652469.2018.1497024