JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Conditional Integral Transforms on a Function Space
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 52, Issue 4,  2012, pp.413-431
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2012.52.4.413
 Title & Authors
Conditional Integral Transforms on a Function Space
Cho, Dong Hyun;
  PDF(new window)
 Abstract
Let be the function space of the vector-valued continuous paths and define and by and , respectively, where < < < . In the present paper, using two simple formulas for the conditional expectations over with the conditioning functions and , we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form where is a complex Borel measure on [0, t] and both and are the Fourier-Stieltjes transforms of the complex Borel measures on .
 Keywords
Analogue of Wiener measure;Conditional Feynman integral;Conditional Fourier-Feynman transform;Conditional Wiener integral;Simple formula for conditional Wiener integral;
 Language
English
 Cited by
 References
1.
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.

2.
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(129)(2004), no. 1, 161-180.

3.
D. H. Cho, Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wiener space: an Lp theory, J. Korean Math. Soc., 41(2004), no. 2, 265-294. crossref(new window)

4.
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)

5.
D. H. Cho, A simple formula for an analogue of conditional Wiener integrals and its applications II, Czechoslovak Math. J., 59(134)(2009), no. 2, 431-452. crossref(new window)

6.
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)

7.
G. W. Johnson and M. L. Lapidus, Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman's operational calculus, Mem. Amer. Math. Soc., 62(1986), no. 351.

8.
H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics, 463, Springer-Verlag, Berlin-New York, 1975.

9.
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)

10.
J. Yeh, Inversion of conditional expectations, Pacific J. Math., 52(1974), 631-640. crossref(new window)

11.
J. Yeh, Inversion of conditional Wiener integrals, Pacific J. Math., 59(1975), no. 2, 623-638. crossref(new window)

12.
J. Yeh, Transformation of conditional Wiener integrals under translation and the Cameron-Martin translation theorem, Tohoku Math. J., 30(2)(1978), no. 4, 505-515. crossref(new window)