Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ON A BANACH ALGEBRA

  • Published : 2004.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

Keywords

References

  1. thesis, University of Minnesota A Functional Transform for Feynman Integrals Similar to the Fourier Transform M.D.Brue
  2. Michigan Math. J. v.23 An $L_{2}$ analytic Fourier-Feynman transform R.H.Cameron;D.A.Storvick https://doi.org/10.1307/mmj/1029001617
  3. Lecture Notes in Math. v.798 Some Banach algebras of analytic Feynman integrable functionals, Analytic Functions Kozubnik, 1979 https://doi.org/10.1007/BFb0097256
  4. Bull. Korean Math. Soc v.21 Evaluation of some conditional Wiener integrals K.S.Chang;J.S.Chang
  5. J. Korean Math. Soc. v.38 no.2 Analytic Fourier-Feynman transform and first variation on abstract Wiener space K.S.Chang;T.S.Song;I.Yoo
  6. Rocky Mountain J. of Math. v.26 no.1 Conditional function space integrals with applications S.J.Chang;D.M.Chung https://doi.org/10.1216/rmjm/1181072102
  7. submitted for publication Multiple $L_{p}$ analytic generalized Fourier-Feynman transforms on the Banach algebra S.J.Chang;J.G.Choi
  8. Trans. Amer. Math. Soc. v.355 no.7 Integration by parts formulas involving generalized Fourier-Feynman transforms on function space S.J.Chang;J.G.Choi;D.Skoug https://doi.org/10.1090/S0002-9947-03-03256-2
  9. Bull. Austral. Math. Soc. v.65 Parts formulas involving conditional Feynman integrals S.J.Chang;D.skoug https://doi.org/10.1017/S0004972700020402
  10. Integral Transforms andSpecial Functions v.14 no.5 Generalized Fourier-Feynman transforms and a first variation on function space https://doi.org/10.1080/1065246031000074425
  11. Pacific J. Math. v.130 Scale invariant measurability in abstract Wiener space D.M.Chung https://doi.org/10.2140/pjm.1987.130.27
  12. J. Korean Math. Soc. v.25 no.1 Conditional Wiener integrals and an integral equation D.M.Chung;S.J.Kang
  13. SIAM J. Math. Anal. v.20 no.4 Conditional analytic Feynman integrals and a related Schrodinger equation D.M.Chung;D.Skoug https://doi.org/10.1137/0520064
  14. Michigan Math. J. v.40 Generalized Feynman integrals via conditional Feynman integrals D.M.Chung;C.Park;D.Skoug https://doi.org/10.1307/mmj/1029004758
  15. Trans. Amer. Math. Soc. v.347 Analytic Fourier-Feynman transforms and convolution T.Huffman;C.Park;D.Skoug https://doi.org/10.2307/2154908
  16. Rocky Mountain J. Math. v.27 Convolution and Fourier-Feynman transforms https://doi.org/10.1216/rmjm/1181071896
  17. Michigan Math J. v.43 Convolution and Fourier-Feynman transforms of functionals involving multiple integrals https://doi.org/10.1307/mmj/1029005461
  18. Oxford Mathematical Monographs The Feynman Integral and Feynman's Operational Calculus G.W.Johnson;M.L.Lapidus
  19. Michigan Math. J. v.26 no.1 An $L_{p}$ analytic Fourier-Feynman transform G.W.Johnson;D.L.Skoug https://doi.org/10.1307/mmj/1029002166
  20. Pacific J. Math v.83 no.1 Scale-invariant measurability in Wiener space https://doi.org/10.2140/pjm.1979.83.157
  21. Journal of Integral Equations and Applications v.3 no.3 A Kac-Feynman integral equation for conditional Wiener integrals C.Park;D.Skoug https://doi.org/10.1216/jiea/1181075633
  22. J. Korean Math. Soc. v.38 no.1 Conditional Fourier-Feynman transforms and conditional convolution products
  23. Stochastic Processes and the Wiener Integral J.Yeh

Cited by

  1. 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
  2. CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM OF FUNCTIONALS IN A FRESNEL TYPE CLASS vol.26, pp.2, 2011, https://doi.org/10.4134/CKMS.2011.26.2.273
  3. 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
  4. Brown–York mass and positive scalar curvature II: Besse’s conjecture and related problems pp.1572-9060, 2019, https://doi.org/10.1007/s10455-019-09653-0