JOURNAL BROWSE
Search
Advanced SearchSearch Tips
FOURIER-FEYNMAN TRANSFORMS FOR FUNCTIONALS IN A GENERALIZED FRESNEL CLASS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
FOURIER-FEYNMAN TRANSFORMS FOR FUNCTIONALS IN A GENERALIZED FRESNEL CLASS
Yoo, Il; Kim, Byoung-Soo;
  PDF(new window)
 Abstract
Huffman, Park and Skoug introduced various results for the analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra S introduced by Cameron and Strovic. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class F(B) which corresponds to S. Recently Kim, Song and Yoo investigated more generalized relationships between the Fourier-Feynman transform and the convolution product for functionals in a generalized Fresnel class containing F(B). In this paper, we establish various interesting relationships and expressions involving the first variation and one or two of the concepts of the Fourier-Feynman transform and the convolution product for functionals in .
 Keywords
abstract Wiener space;generalized Fresnel class;analytic Feynman integral;Fourier-Feynman transform;convolution;first variation;
 Language
English
 Cited by
1.
FOURIER-FEYNMAN TRANSFORMS FOR FUNCTIONALS IN A GENERALIZED FRESNEL CLASS,;;

대한수학회논문집, 2007. vol.22. 1, pp.75-90 crossref(new window)
 References
1.
J. M. Ahn, K. S. Chang, B. S. Kim, and I. Yoo, Fourier-Feynman transform, convolution and first variation, Acta Math. Hungar. 100 (2003), 215-235 crossref(new window)

2.
S. Albeverio and R. Hoegh-Krohn, Mathematical theory of Feynman path integrals, Lecture Notes in Math. 523, Springer-Verlag, Berlin, 1976

3.
M. D. Brue, A functional transform for Feynman integrals similar to the Fourier transform, Thesis, Univ. of Minnesota, Minneapolis, 1972

4.
R. H. Cameron and D. A. Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1-30 crossref(new window)

5.
R. H. Cameron and D. A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, Analytic functions, (Kozubnik, 1979), Lecture Notes in Math. 798, pp. 18-27, Springer-Verlag, Berlin, 1980 crossref(new window)

6.
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), 823-842 crossref(new window)

7.
K. S. Chang, B. S. Kim, and I. Yoo, Fourier-Feynman transform, convolution and first variation of functionals on abstract Wiener space, Integral Transforms and Special Functions 10 (2000), 179-200 crossref(new window)

8.
L. Gross, Abstract Wiener spaces, Proc. 5th Berkley Sym. Math. Stat. Prob. 2 (1965), 31-42

9.
T. Huffman, C. Park, and D. Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), 661-673 crossref(new window)

10.
T. Huffman, C. Park, and D. Skoug, Convolutions and Fourier-Feynman transforms of functionals involving multiple integrals, Michigan Math. J. 43 (1996), 247-261 crossref(new window)

11.
T. Huffman, C. Park, and D. Skoug, Convolution and Fourier-Feynman transforms, Rocky Mountain J. Math. 27 (1997), 827-841 crossref(new window)

12.
G. W. Johnson and D. L. Skoug, An $L_p$ analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), 103-127 crossref(new window)

13.
G. Kallianpur and C. Bromley, Generalized Feynman integrals using analytic continuation in several complex variables, in 'Stochastic Analysis and Application (ed. M.H.Pinsky)', Marcel-Dekker Inc., New York, 1984

14.
G. Kallianpur, D. Kannan, and R. L. Karandikar, Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces and a Cameron-Martin formula, Ann. Inst. Henri. Poincare 21 (1985), 323-361

15.
B. S. Kim, T. S. Song, and I. Yoo, Fourier-Feynman transforms for functionals in a generalized Fresnel class, submitted crossref(new window)

16.
H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Math. 463, Springer-Verlag, Berlin, 1975

17.
C. Park, D. Skoug, and D. Storvick, Relationships among the first variation, the convolution product, and the Fourier-Feynman transform, Rocky Mountain J. Math. 28 (1998), 1447-1468 crossref(new window)

18.
D. Skoug and D. Storvick, A survey results involving transforms and convolutions in function space, Rocky Mountain J. Math. 34 (2004), 1147-1176 crossref(new window)

19.
J. Yeh, Convolution in Fourier-Wiener transform, Pacific J. Math. 15 (1965), 731-738 crossref(new window)

20.
I. Yoo, Convolution and the Fourier-Wiener transform on abstract Wiener space, Rocky Mountain J. Math. 25 (1995), 1577-1587 crossref(new window)

21.
I. Yoo, Notes on a Generalized Fresnel Class, Appl. Math. Optim. 30 (1994), 225-233 crossref(new window)