논문KCI 등재
A Fubini theorem for generalized analytic Feynman integral on function space
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Abstract. In this paper we establish a Fubini theorem for generalized analytic Feynman integral and L1 generalized analytic Fourier-Feynman transform for the functional of the form [수식] where {α1, . . . , αm} is an orthonormal set of functions from L2 a,b[0, T]. We then obtain several generalized analytic Feynman integration formulas involving generalized analytic Fourier-Feynman transforms.
Abstract
Abstract. In this paper we establish a Fubini theorem for generalized analytic Feynman integral and L1 generalized analytic Fourier-Feynman transform for the functional of the form [수식] where {α1, . . . , αm} is an orthonormal set of functions from L2 a,b[0, T]. We then obtain several generalized analytic Feynman integration formulas involving generalized analytic Fourier-Feynman transforms.
참고문헌 (13)
- M. D. Brue, "A functional transform for Feynman integrals similar to the Fourier trans- form", 석사, pp.1972
- R. H. Cameron, "An L2 analytic Fourier-Feynman transform", Michi- gan Math. J, 23(1), pp.1~30 (1976)
- S. J. Chang, "Conditional function space integrals with applications", Rocky Mountain J. Math, 26(1), pp.37~62 (1996)
- S. J. Chang, "Integration by parts formulas involving gen- eralized Fourier-Feynman transforms on function space", Trans. Amer. Math. Soc, 355(7), pp.2925~2948 (2003)
- 장승준, "A Fubini theorem for generalized analytic Feynman integrals and Fourier-Feynman transforms on function space", 대한수학회보, 40(3), pp.437~456 (2003), 대한수학회
- D. M. Chung, "Scale-invariant measurability in abstract Wiener spaces", Pacific J. Math, 130(1), pp.27~40 (1987)
- T. Huffman, "A Fubini theorem for analytic Feynman integrals with applications", J. Korean Math. Soc, 38(2), pp.409~420 (2001)
- T. Huffman, "Integration formulas involving Fourier-Feynman transforms via a Fubini theo- rem", J. Korean Math. Soc, 38(2), pp.421~435 (2001)
- G. W. Johnson, "An Lp analytic Fourier-Feynman transform", Michigan Math. J, 26(1), pp.103~127 (1979)
- G. W. Johnson, "Scale-invariant measurability in Wiener space", Pacific J. Math, 83(1), pp.157~176 (1979)
- E. Nelson, "Dynamical Theories of Brownian Motion" (1967), Princeton University Press
- J. Yeh, "Singularity of Gaussian measures on function spaces induced by Brownian mo- tion processes with non-stationary increments", Illinois J. Math, 15, pp.37~46 (1971)
- J. Yeh, "Stochastic Processes and the Wiener Integral" (1973), Marcel Dekker, Inc.
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