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Conditional integrals on abstract Wiener and Hilbert spaceswith application to Feynman integrals

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In this paper, we define conditional integrals on abstract Wiener and Hilbert spaces and then obtain a formula for evaluating the integrals. We use this formula to establish the existence of conditional Feynman integrals for the classes Λq(B) and Λq(H) of functions on abstract Wiener and Hilbert spaces and then specialize this result to provide the fundamental solution to the Schr¨odinger equation with the forced harmonic oscillator.

Abstract

In this paper, we define conditional integrals on abstract Wiener and Hilbert spaces and then obtain a formula for evaluating the integrals. We use this formula to establish the existence of conditional Feynman integrals for the classes Λq(B) and Λq(H) of functions on abstract Wiener and Hilbert spaces and then specialize this result to provide the fundamental solution to the Schr¨odinger equation with the forced harmonic oscillator.

참고문헌 (21)

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  6. "Conditional analytic Feynman integrals for the Fresnel class of functions on abstract Wiener space" (1990)
  7. "Conditional analytic Feynman integrals on abstract Wiener space" (1991)
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  10. "Integration in functional spaces" (1960)
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  12. "Generalized uniform complex measure in the Hilbertian metric space withtheir applications to Feynman path integrals" (1976)
  13. "The equivalence of two approaches to the Feynman integral" (1982)
  14. "The Feynman integral and Feynman?s operational calculus" (2000), Oxford Univ. press
  15. "Scale-invariant measurability in Wiener space" (1979)
  16. "Notes on the Feynman integral III PacificJ. of Math. 105" (1983)
  17. "Analytic and sequential Feynmanintegrals on abstract Wiener and Hilbert spaces and a Cameron-Martin formula" (1985)
  18. "Gaussian measures in Banach Spaces" (1975), Springer-Verlag
  19. "A simple formula for conditional Wiener integrals withapplications" (1988)
  20. "Conditional Yeh-Wiener integrals with vector-valued Conditioning Functions" (1989)
  21. "Inversion of Conditional Wiener Integrals" (1975)

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