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GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS
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 Title & Authors
GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS
Chang, Seung-Jun; Lee, Il-Yong;
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 Abstract
In this paper, we de ne an analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra ([0, T]) which is called the Fresnel type class, and in more general class of functionals de ned on general functio space [0, T] rather than on classical Wiener space. Also we obtain some relationships between the analytic generalized Fourier-Feynman transform and convolution product for functionals in ([0, T]) and in .
 Keywords
generalized Brownian motion process;generalized analytic Feynman integral;generalized analytic Fourier-Feynman transform;convolution product;Fresnel type class;
 Language
English
 Cited by
 References
1.
J. M. Ahn, $L_1$ analytic Fourier-Feynman transform on the Fresnel class of abstract Wiener space, Bull. Korean Math. Soc. 35 (1998), no. 1, 99-117.

2.
M. D. Brue, A functional transform for Feynman integrals similar to the Fourier transform, Thesis, Univ. of Minnesota, Minneapolis, 1972.

3.
R. H. Cameron and D. A. Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), no. 1, 1-30. crossref(new window)

4.
S. J. Chang and J. G. Choi, Multiple $L_p$ analytic generalized Fourier-Feynman transform on the Banach algebra, Commun. Korean Math. Soc. 19 (2004), no. 1, 93-111. crossref(new window)

5.
S. J. Chang, J. G. Choi, and D. Skoug, Integration by parts formulas involving generalized Fourier-Feynman transforms on function space, Trans. Amer. Math. Soc. 355 (2003), no. 7, 2925-2948. crossref(new window)

6.
S. J. Chang and D. M. Chung, Conditional function space integrals with applications, Rocky Mountain J. Math. 26 (1996), no. 1, 37-62. crossref(new window)

7.
K. S. Chang, B. S. Kim, and I. Yoo, Analytic Fourier-Feynman transform and convolution of functionals on abstract Wiener space, Rocky Mountain J. Math. 30 (2000), no. 3, 823-842. crossref(new window)

8.
S. J. Chang and D. Skoug, Generalized Fourier-Feynman transforms and a first variation on function space, Integral Transforms Spec. Funct. 14 (2003), no. 5, 375-393. crossref(new window)

9.
S. J. Chang and I. Y. Lee, Multiple $L_p$ analytic generalized Fourier-Feynman transform on a Fresnel type class, J. Chungcheong Math. Soc. 19 (2006), 79-99.

10.
S. J. Chang and I. Y. Lee, Generalized Fourier-Feynman transforms and conditional generalized Fourier-Feynman transforms on a Fresnel type class, submitted for publication.

11.
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.

12.
D. M. Chung, Scale-invariant measurability in abstract Wiener space, Pacific J. Math. 130 (1987), no. 1, 27-40. crossref(new window)

13.
T. Huffman, C. Park, and D. Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), no. 2, 661-673. crossref(new window)

14.
T. Huffman, C. Park, and D. Skoug, Convolutions and Fourier-Feynman transforms of functionals involving multiple integrals, Michigan Math. J. 43 (1996), no. 2, 247-261. crossref(new window)

15.
T. Huffman, C. Park, and D. Skoug, Convolution and Fourier-Feynman transforms, Rocky Mountain J. Math. 27 (1997), no. 3, 827-841. crossref(new window)

16.
G. W. Johnson and D. L. Skoug, An $L_p$ analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), no. 1, 103-127. crossref(new window)

17.
G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), no. 1, 157-176. crossref(new window)

18.
G. Kallianpur and C. Bromley, Generalized Feynman integrals using analytic continuation in several complex variables, in Stochastic analysis and applications, 217-267, Adv. Probab. Related Topics, 7, Dekker, New York, 1984.

19.
H.-H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer-Verlag, Berlin, 1975.

20.
J. Yeh, Convolution in Fourier-Wiener transform, Pacific J. Math. 15 (1965), 731-738. crossref(new window)

21.
J. Yeh, Stochastic Processes and the Wiener Integral, Marcel Dekker, Inc., New York, 1973.

22.
I. Yoo, Convolution and the Fourier-Wiener transform on abstract Wiener space, Rocky Mountain J. Math. 25 (1995), no. 4, 1577-1587. crossref(new window)