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2005 | 3 | 3 | 475-495
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Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we evaluate various analytic Feynman integrals of first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of cylinder type functions defined over Wiener paths in abstract Wiener space. We also derive the analytic Feynman integral of the conditional Fourier-Feynman transform for the product of the cylinder type functions which define the functions in a Banach algebra introduced by Yoo, with n linear factors.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
3
Strony
475-495
Opis fizyczny
Daty
wydano
2005-09-01
online
2005-09-01
Twórcy
autor
Bibliografia
  • [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 infefineite Wiener integral, Proc. Amer. Math. Soc., Vol. 2, (1951), pp. 914–924. http://dx.doi.org/10.2307/2031708
  • [3] R.H. Cameron and D.A. Storvick: “An L 2 analytic Fourier-Feynman transform”, Michigan Math. J., Vol. 23, (1976), pp. 1–30. http://dx.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., Vol. 798, Springer, 1980, pp. 18–27. http://dx.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 abstract Wiener space”, Integral Transform. Spec. Funct., Vol. 14(3), (2003), pp. 217–235. http://dx.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”, Intern. Math. J., Vol. 2(9), (2002), pp. 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., Vol. 54(129), (2004), pp. 161–180. http://dx.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., Vol. 38(2), (2001), pp. 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., Vol. 42(2), (2004), pp. 265–294.
  • [10] D.H. Cho: “Conditional first variation over Wiener paths in abstract Wiener space”, J. Korean Math. Soc., (2004), to appear.
  • [11] D.H. Cho: “Fourier-Feynman transform and first variation of cylinder type functions over Wiener paths in abstract Wiener space”, Intern. Math. J., (2004), submitted.
  • [12] D.H. Cho: “Conditional Fourier-Feynman transforms of variations over Wiener paths in abstract Wiener space”, J. Korean Math. Soc., (2005), to apear.
  • [13] G.W. Johnson and D.L. Skoug: “An L p analytic Fourier-Feynman transform”, Michigan Math. J., Vol. 26, (1979), pp. 103–127. http://dx.doi.org/10.1307/mmj/1029002166
  • [14] G. Kallianpur and C. Bromley: “Generalized Feynman integrals using an analytic continuation in several complex variables”, In Stochastic analysis and applications, Adv. Probab.Related Topics, Vol. 7, Dekker, New York, 1984, pp. 217–267.
  • [15] H.H. Kuo: Gaussian measures in Banach spaces, Lecture Notes in Math., Vol. 463, Springer, 1975.
  • [16] C. Park, D.L. Skong and D.A. Storvick: “Fourier-Feynman transforms and the frist variation”, Rend. Circ. Mat. Palermo II, Vol. 47(2), (1998), pp. 277–292.
  • [17] K.S. Ryu: “The Wiener integral over paths in abstract Wiener space”, J. Korean Math. Soc., Vol. 29(2), (1992), pp. 317–331.
  • [18] I. Yoo: “The analytic Feynman integral over paths in abstract Wiener space”, Comm. Korean Math. Soc., Vol. 10(1), (1995), pp. 93–107.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475918
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