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http://dx.doi.org/10.4134/JKMS.2006.43.5.967

CONDITIONAL FOURIER-FEYNMAN TRANSFORMS OF VARIATIONS OVER WIENER PATHS IN ABSTRACT WIENER SPACE  

Cho, Dong-Hyun (Department of Mathematics Kyonggi University)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.5, 2006 , pp. 967-990 More about this Journal
Abstract
In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.
Keywords
conditional Feynman integral; conditional first variation; conditional Fourier-Feynman transform; conditional Wiener integral; Feynman integral; first variation; Fourier-Feynman transform; Wiener integral; Wiener paths in abstract Wiener space;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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1 J. Kuelbs, Abstract Wiener measure and applications to analysis, Pacific J. Math. 31 (1969), no. 2, 433-450   DOI
2 H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics, Vol. 463. Springer-Verlag, Berlin-New York, 1975
3 C. Park, D. L. Skoug, and D. A. Storvick, Fourier-Feynman transfroms and the first variation, Rend. Circ. Mat. Palermo 47 (1998), no. 2, 277-292   DOI
4 I. Yoo, The analytic Feynman integral over paths in abstract Wiener space, Com- mun. Korean Math. Soc. 10 (1995), no. 1, 93-107   과학기술학회마을
5 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. 41 (2004), no. 2, 265-294   DOI   ScienceOn
6 K. S. Chang, T. S. Song and I. Yoo, Analytic Fourier-Feynman transform and first variation on abstract Wiener space, J. Korean Math. Soc. 38 (2001), no. 2, 485-501
7 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 ab- stract Wiener space, Integral Transform. Spec. Funct. 14 (2003), no. 3, 217-235   DOI   ScienceOn
8 K. S. Chang, D. H. Cho, and I. Yoo, A conditional analytic Feynman integral over Wiener paths in abstract Wiener space, Int. Math. J. 2 (2002), no. 9, 855-870
9 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. 54 (2004), no. 129, 161- 180   DOI
10 D. H. Cho, Conditional first variation over Wiener paths in abstract Wiener space, J. Korean Math. Soc. 42 (2005), no. 5, 1031-1056   DOI   ScienceOn
11 G. B. Folland, Real analysis, John Wiley & Sons, 1984
12 G. W. Johnson and D. L. Skoug, An Lp analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), 103-127   DOI
13 R. H. Cameron and D. A. Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1-30   DOI
14 D. H. Cho, Fourier-Feynman transform and first variation of cylinder type functions over Wiener paths in abstract Wiener space, Int. Math. J. (2005), to appear
15 R. H. Cameron and D. A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, An analytic functions, Lecture Notes in Math. 798 (1980), 18-27   DOI
16 G. Kallianpur and C. Bromley, Generalized Feynman integrals using an analytic continuation in several complex variables, Stochastic Analysis and Applications, Dekker, 1984
17 R. H. Cameron, The first variation of an indefinite Wiener intergal, Proc. Amer. Math. Soc. 2 (1951), 914-924
18 K. S. Ryu, The Wiener integral over paths in abstract Wiener space, J. Korean Math. Soc. 29 (1992), no. 2, 317-331
19 M. D. Brue, A functional transform for Feynman integrals similar to the Fourier transform, thesis, Univ. of Minnesota, Minneapolis, 1972