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Generalized Fourier–Feynman Transform of Bounded Cylinder Functions on the Function Space C_(a,b)[0, T]

최재길
경북대학교 자연과학대학 수학과|2024.06|Kyungpook Mathematical Journal|제64권 제2호|pp. 219-233|DOI 10.5666/KMJ.2024.64.2.219

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참고문헌

키워드

generalized Brownian motion processgeneralized analytic Feynman integralgeneral Wiener spacegeneralized analytic Fourier–Feynman transformcylinder function
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초록

In this paper, we study the generalized Fourier–Feynman transform (GFFT) for functions on the general Wiener space Ca,b[0, T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on Ca,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on Ca,b[0, T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions.

Abstract

In this paper, we study the generalized Fourier–Feynman transform (GFFT) for functions on the general Wiener space Ca,b[0, T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on Ca,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on Ca,b[0, T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions.

참고문헌 (20)

  1. M. D. Brue, "A Functional Transform for Feynman Integrals Similar to the Fourier Transform", Ph.D., pp.1972
  2. R. H. Cameron, "An L2 analytic Fourier–Feynman transform", Michigan Math. J., 23, pp.1~30 (1976)
  3. R. H. Cameron, "Analytic Feynman integral solutions of an integral equation related to the Schroedinger equation", J. Anal. Math., 38, pp.34~66 (1980)
  4. R. H. Cameron, "Analytic Functions (Proc. Seventh Conf., Kozubnik, 1979)", pp.18~67 (1980), Springer
  5. K. S. Chang, "Necessary and sufficient conditions for the Fresnel integrability of certain classes of functions", J. Korean Math. Soc., 21(1), pp.21~29 (1984)
  6. K. S. Chang, "Necessary and sufficient conditions for membership in the Banach algebras S for certain classes of functions", Rend. Circ. Mat. Palermo (2) Suppl., 17, pp.153~171 (1987)
  7. K. S. Chang, "Functions in the Fresnel class", Proc. Amer. Math. Soc., 100, pp.309~318 (1987)
  8. S. J. Chang, "Generalized Fourier–Feynman transform and sequential transforms on function space", J. Korean Soc. Math, 49, pp.1065~1082 (2012)
  9. S. J. Chang, "Integration by parts formulas involving generalized Fourier–Feynman transforms on function space", Trans. Amer. Math. Soc., 355, pp.2925~2948 (2003)
  10. S. J. Chang, "Evaluation formulas for conditional function space integrals I", Stoch. Anal. Appl., 25, pp.141~168 (2007)
  11. S. J. Chang, "Generalized Fourier–Feynman transforms and a first variation on function space", Integral Transforms Spec. Funct., 14, pp.375~393 (2003)
  12. J. G. Choi, "Generalized analytic Fourier–Feynman transform of functionals in a Banach algebra F_(A1,A2)^(a,b)", J. Funct. Spaces Appl., 2013, pp.1~12 (2013)
  13. D. M. Chung, "Cylinder functions in the Fresnel class of functions on abstract Wiener spaces", Proc. Amer. Math. Soc., 115, pp.381~388 (1992)
  14. T. Huffman, "Analytic Fourier–Feynman transforms and convolution", Trans. Amer. Math. Soc., 347, pp.661~673 (1995)
  15. G. W. Johnson, "An Lp analytic Fourier–Feynman transform", Michigan Math. J., 26, pp.103~127 (1979)
  16. G. W. Johnson, "Scale-invariant measurability in Wiener space", Pacific J. Math., 83, pp.157~176 (1979)
  17. G. W. Johnson, "Notes on the Feynman integral, III: The Schroedinger equation", Pacific J. Math., 105, pp.321~358 (1983)
  18. D. Skoug, "A survey of results involving transforms and convolutions in function space", Rocky Mountain J. Math., 34, pp.1147~1175 (2004)
  19. J. Yeh, "Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments", Illinois J. Math., 15, pp.37~46 (1971)
  20. J. Yeh, "Stochastic Processes and the Wiener Integral" (1973), Marcel Dekker Inc.

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