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Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wiener space : an{L}$_{\text{p}}$ theory

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Abstract

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier- Feynman transforms. Also, we evaluate the conditional Fourier- Feynman transforms of the functions of the forms exp T 0 θ(s, x(s))ds, exp T 0 θ(s, x(s))dsφ(x(T)), exp T 0 θ(s, x(s))dζ(s), exp T 0 θ(s, x(s))dζ(s)φ(x(T)) which are of interest in Feynman integration theories and quantum mechanics.

참고문헌 (15)

  1. "Some Banach algebras of analytic Feynmanintegrable functionals", Springer-Verlag
  2. "Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wienerspace", 14(3), pp.217~235 (2003)
  3. "A conditional anlytic Feynmanintegral over Wiener paths"
  4. "Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space", 13, pp.345~362 (2002)
  5. "The eect of drift on conditional Fourier-Feynmantransforms and conditional convolution products", 2(4), pp.505~527 (2000)
  6. "Generalized Feynman integrals using analyticcontinuation in several complex variables" (1984)
  7. "The law of the iterated logarithm for Brownian motionin a Banach space" (1973)
  8. "Gaussian measures in Banach spaces Lecture Notes in Math. 463" (1975), Springer-Verlag
  9. "A simple formula for conditional Wiener integrals withapplications" (1988)
  10. "Conditional Fourier-Feynman transforms and conditional convolutionproducts", 38(1), pp.61~76 (2001)
  11. "The Wiener integral over paths in abstract Wiener space" (1992)
  12. "Introduction to Fourier analysis on Euclidean spaces" (1971), Princeton Univ. Press
  13. "Inversion of conditional expectations" (1974)
  14. "Inversion of conditional Wiener integrals" (1975)
  15. "The analytic Feynman integral over paths in abstract Wiener space", 10(1), pp.93~107 (1995)

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