DOI QR코드

DOI QR Code

A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRALS AND FOURIER-FEYNMAN TRANSFORMS ON FUNCTION SPACE

  • Published : 2003.08.01

Abstract

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

Keywords

generalized Brownian motion process;generalized analytic Feynman integral;generalized analytic Fourier-Feynman transform;Fubinitheorem

References

  1. Lecture Notes in Math. v.798 Some Banach algebras of analytic Feynman integrable functionals https://doi.org/10.1007/BFb0097256
  2. Michigan Math. J. v.26 An Lp analytic Fourier-Feynman transform G.W.Johnson;D.L.Skoug https://doi.org/10.1307/mmj/1029002166
  3. Int. J. Math. Math. Sci. v.23 Conditional generalized analytic Feynman integrals and a generalized integral equation S.J.Chang;S.J.Kang;D.Skoug https://doi.org/10.1155/S0161171200002775
  4. Pacific J. Math. v.130 Scale-invariant measurability in abstract Wiener spaces D.M.Chung https://doi.org/10.2140/pjm.1987.130.27
  5. Stochastic processes and the Wiener integral J.Yeh
  6. J. Korean Math. Soc. v.38 A Fubini theorem for analytic Feynman integrals with applications T.Huffman;D.Skoug;D.Storvick
  7. Generalized Fourier-Feynman transforms and a first variation on function space, to appear in the Integral transforms and special functions S.J.Chang;D.Skoug
  8. J. Korean Math. Soc. v.38 Integration formulas involving Fourier-Feynman transforms via a Fubini theorem
  9. Pacific J. Math. v.83 Scale-invariant measurability in Wiener space https://doi.org/10.2140/pjm.1979.83.157
  10. A functional transform for Feynman integrals similar to the Fourier transforms M.D.Brue
  11. J. Korean Math. Soc. v.19 Scale-invariant measurability in Yeh-Wiener space K.S.Chang
  12. Int. J. Math. Math. Sci. v.29 Relationships of convolution products, generalized transforms and the first variation on function space S.J.Chang;J.G.Choi https://doi.org/10.1155/S0161171202006361
  13. The Feynman Integral and Feynman's Operational Calculus G.W.Johnson;M.L.Lapidus
  14. Rocky Mountain J. Math. v.26 Conditional function space integrals with applications S.J.Chang;D.M.Chung https://doi.org/10.1216/rmjm/1181072102
  15. Rocky Mountain J. Math. v.30 Translation theorems for Fourier-Feynman transforms and conditional Fourier-Feynman transforms S.J.Chang;C.Park;D.Skoug https://doi.org/10.1216/rmjm/1022009276
  16. Michigan Math. J. v.23 An L₂ analytic Fourier-Feynman trasform R.H.Cameron;D.A.Storvick https://doi.org/10.1307/mmj/1029001617

Cited by

  1. A new aspect of the analytic Fourier-Feynman transform and its applications vol.26, pp.1, 2015, https://doi.org/10.1080/10652469.2014.975128
  2. A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRAL ON FUNCTION SPACE vol.50, pp.1, 2013, https://doi.org/10.4134/BKMS.2013.50.1.217
  3. Some relationships for the double modified generalized analytic function space Fourier-Feynman transform and its applications vol.290, pp.4, 2017, https://doi.org/10.1002/mana.201500369
  4. generalized analytic Fourier–Feynman transform vol.29, pp.9, 2018, https://doi.org/10.1080/10652469.2018.1497024