대한수학회지 (Journal of the Korean Mathematical Society)

  • 제43권5호
  • /
  • Pages.967-990
  • /
  • 2006
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

CONDITIONAL FOURIER-FEYNMAN TRANSFORMS OF VARIATIONS OVER WIENER PATHS IN ABSTRACT WIENER SPACE

  • 발행 : 2006.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.

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, The first variation of an indefinite Wiener intergal, Proc. Amer. Math. Soc. 2 (1951), 914-924
  3. R. H. Cameron and D. A. Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1-30 https://doi.org/10.1307/mmj/1029001617
  4. R. H. Cameron and D. A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, An analytic functions, Lecture Notes in Math. 798 (1980), 18-27 https://doi.org/10.1007/BFb0097256
  5. K. S. Chang, D. H. Cho, B. S. Kim, T. S. Song, and I. Yoo, Conditional Fourier-Feynman transform and convolution product over Wiener paths in ab- stract Wiener space, Integral Transform. Spec. Funct. 14 (2003), no. 3, 217-235 https://doi.org/10.1080/1065246031000081652
  6. K. S. Chang, D. H. Cho, and I. Yoo, A conditional analytic Feynman integral over Wiener paths in abstract Wiener space, Int. Math. J. 2 (2002), no. 9, 855-870
  7. K. S. Chang, D. H. Cho, and I. Yoo, Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space, Czechoslovak Math. J. 54 (2004), no. 129, 161- 180 https://doi.org/10.1023/B:CMAJ.0000027256.06816.1a
  8. K. S. Chang, T. S. Song and I. Yoo, Analytic Fourier-Feynman transform and first variation on abstract Wiener space, J. Korean Math. Soc. 38 (2001), no. 2, 485-501
  9. D. H. Cho, Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wiener space : an $L_p$ theory, J. Korean Math. Soc. 41 (2004), no. 2, 265-294 https://doi.org/10.4134/JKMS.2004.41.2.265
  10. D. H. Cho, Conditional first variation over Wiener paths in abstract Wiener space, J. Korean Math. Soc. 42 (2005), no. 5, 1031-1056 https://doi.org/10.4134/JKMS.2005.42.5.1031
  11. D. H. Cho, Fourier-Feynman transform and first variation of cylinder type functions over Wiener paths in abstract Wiener space, Int. Math. J. (2005), to appear
  12. G. B. Folland, Real analysis, John Wiley & Sons, 1984
  13. G. W. Johnson and D. L. Skoug, An Lp analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), 103-127 https://doi.org/10.1307/mmj/1029002166
  14. G. Kallianpur and C. Bromley, Generalized Feynman integrals using an analytic continuation in several complex variables, Stochastic Analysis and Applications, Dekker, 1984
  15. J. Kuelbs, Abstract Wiener measure and applications to analysis, Pacific J. Math. 31 (1969), no. 2, 433-450 https://doi.org/10.2140/pjm.1969.31.433
  16. H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics, Vol. 463. Springer-Verlag, Berlin-New York, 1975
  17. C. Park, D. L. Skoug, and D. A. Storvick, Fourier-Feynman transfroms and the first variation, Rend. Circ. Mat. Palermo 47 (1998), no. 2, 277-292 https://doi.org/10.1007/BF02844368
  18. K. S. Ryu, The Wiener integral over paths in abstract Wiener space, J. Korean Math. Soc. 29 (1992), no. 2, 317-331
  19. I. Yoo, The analytic Feynman integral over paths in abstract Wiener space, Com- mun. Korean Math. Soc. 10 (1995), no. 1, 93-107

피인용 문헌

  1. A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE vol.53, pp.5, 2016, https://doi.org/10.4134/JKMS.j150317