JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CONDITIONAL FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS OF UNBOUNDED FUNCTIONS ON A GENERALIZED WIENER SPACE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CONDITIONAL FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS OF UNBOUNDED FUNCTIONS ON A GENERALIZED WIENER SPACE
Cho, Dong Hyun;
  PDF(new window)
 Abstract
Let C[0, ] denote the function space of real-valued continuous paths on [0, ]. Define and by $X_n(x)
 Keywords
analogue of Wiener space;analytic conditional Feynman integral;analytic conditional Fourier-Feynman transform;analytic conditional Wiener integral;conditional convolution product;Wiener space;
 Language
English
 Cited by
1.
A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE, Journal of the Korean Mathematical Society, 2016, 53, 5, 991  crossref(new windwow)
 References
1.
M. D. Brue, A functional transform for Feynman integrals similar to the Fourier transform, Thesis, Univ. of Minnesota, Minneapolis, 1972.

2.
R. H. Cameron and D. A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, Lecture Notes in Mathematics 798, Springer, Berlin-New York, 1980.

3.
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 abstract Wiener space, Integral Transforms Spec. Funct. 14 (2003), no. 3, 217-235. crossref(new window)

4.
S. J. Chang and D. M. Chung, A class of conditional Wiener integrals, J. Korean Math. Soc. 30 (1993), no. 1, 161-172.

5.
S. J. Chang and D. Skoug, The effect of drift on conditional Fourier-Feynman trans- forms and conditional convolution products, Int. J. Appl. Math. 2 (2000), no. 4, 505-527.

6.
S. J. Chang and D. Skoug, The effect of drift on the Fourier-Feynman transform, the convolution product and the first variation, Panamer. Math. J. 10 (2000), no. 2, 25-38.

7.
D. H. Cho, A time-independent conditional Fourier-Feynman transform and convolution product on an analogue of Wiener space, Honam Math. J. (2013), submitted. crossref(new window)

8.
D. H. Cho, A time-dependent conditional Fourier-Feynman transform and convolution product on an analogue of Wiener space, Houston J. Math. (2012), submitted.

9.
D. H. Cho, Conditional integral transforms and convolutions of bounded functions on an analogue of Wiener space, J. Chungcheong Math. Soc. (2012), to appear.

10.
D. H. Cho, Conditional integral transforms and conditional convolution products on a function space, Integral Transforms Spec. Funct. 23 (2012), no. 6, 405-420. crossref(new window)

11.
D. H. Cho, A simple formula for an analogue of conditional Wiener integrals and its applications II, Czechoslovak Math. J. 59 (2009), no. 2, 431-452. crossref(new window)

12.
D. H. Cho, A simple formula for an analogue of conditional Wiener integrals and its applications, Trans. Amer. Math. Soc. 360 (2008), no. 7, 3795-3811. crossref(new window)

13.
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. crossref(new window)

14.
D. H. Cho, B. J. Kim, and I. Yoo, Analogues of conditional Wiener integrals and their change of scale transformations on a function space, J. Math. Anal. Appl. 359 (2009), no. 2, 421-438. crossref(new window)

15.
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)

16.
M. K. Im and K. S. Ryu, An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39 (2002), no. 5, 801-819. crossref(new window)

17.
G. W. Johnson and D. L. Skoug, The Cameron-Storvick function space integral: an L $(L_p,L_p{\prime})$ theory, Nagoya Math. J. 60 (1976), 93-137.

18.
M. J. Kim, Conditional Fourier-Feynman transform and convolution product on a func- tion space, Int. J. Math. Anal. 3 (2009), no. 10, 457-471.

19.
B. J. Kim, B. S. Kim, and D. Skoug, Conditional integral transforms, conditional convolution products and first variations, Panamer. Math. J. 14 (2004), no. 3, 27-47.

20.
C. Park and D. Skoug, Conditional Fourier-Feynman transforms and conditional convolution products, J. Korean Math. Soc. 38 (2001), no. 1, 61-76.

21.
C. Park and D. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), no. 2, 381-394. crossref(new window)

22.
K. S. Ryu and M. K. Im, A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula, Trans. Amer. Math. Soc. 354 (2002), no. 12, 4921-4951. crossref(new window)

23.
K. S. Ryu, M. K. Im, and K. S. Choi, Survey of the theories for analogue of Wiener measure space, Interdiscip. Inform. Sci. 15 (2009), no. 3, 319-337.