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GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS
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 Title & Authors
GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS
Chang, Seung-Jun; Choi, Jae-Gil; Chung, Hyun-Soo;
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 Abstract
In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x)
 Keywords
generalized Brownian motion;generalized analytic Feynman integral;function space integral;cylinder functional;change of scale formula;
 Language
English
 Cited by
1.
GENERALIZED FOURIER-FEYNMAN TRANSFORM AND SEQUENTIAL TRANSFORMS ON FUNCTION SPACE,;;

대한수학회지, 2012. vol.49. 5, pp.1065-1082 crossref(new window)
1.
Change of path formula on the function space with applications, Indagationes Mathematicae, 2014, 25, 3, 596  crossref(new windwow)
2.
A Modified Analytic Function Space Feynman Integral and Its Applications, Journal of Function Spaces, 2014, 2014, 1  crossref(new windwow)
 References
1.
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)

2.
R. H. Cameron and D. A. Storvick, Relationships between the Wiener integral and the analytic Feynman integral, Rend. Circ. Mat. Palermo (2) Suppl. No. 17 (1987), 117-133.

3.
R. H. Cameron and D. A. Storvick, Change of scale formulas for Wiener integral, Rend. Circ. Mat. Palermo (2) Suppl. No. 17 (1987), 105-115.

4.
K. S. Chang, G. W. Johnson, and D. L. Skoug, Necessary and sufficient conditions for the Fresnel integrability of certain classes of functions, J. Korean Math. Soc. 21 (1984), no. 1, 21-29.

5.
K. S. Chang, G. W. Johnson, and D. L. Skoug, Necessary and sufficient conditions for membership in the Banach algebra S for certain classes of functions, Rend. Circ. Mat. Palermo (2) Suppl. No. 17 (1987), 153-171.

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.
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)

8.
S. J. Chang, J. G. Choi, and D. Skoug, Evaluation formulas for conditional function space integrals. I, Stoch. Anal. Appl. 25 (2007), no. 1, 141-168. crossref(new window)

9.
S. J. Chang and D. Skoug, Generalized Fourier-Feynman transforms and a rst variation on function space, Integral Transforms Spec. Funct. 14 (2003), no. 5, 375-393. crossref(new window)

10.
B. S. Kim and T. S. Kim, Change of scale formulas for Wiener integral over paths in abstract Wiener space, Commun. Korean Math. Soc. 21 (2006), no. 1, 75-88. crossref(new window)

11.
Y. S. Kim, Analytic Feynman integrals, Fourier-Feynman transforms and change of scale formula for Wiener integrals over paths on abstract Wiener spaces, Integral Transforms Spec. Funct. 16 (2005), no. 4, 323-335. crossref(new window)

12.
Y. S. Kim, J. M. Ahn, K. S. Chang, and I. Yoo, A change of scale formula for Wiener integrals on the product abstract Wiener spaces, J. Korean Math. Soc. 33 (1996), no. 2, 269-282.

13.
H. L. Royden, Real Analysis, Third edition, Macmillan, 1988.

14.
J. Yeh, Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments, Illinois J. Math. 15 (1971), 37-46.

15.
J. Yeh, Stochastic Processes and the Wiener Integral, Marcel Dekker, Inc., New York, 1973.

16.
I. Yoo, Sequential Yeh-Feynman integrals, Doctoral Thesis, Yonsei University, 1987.

17.
I. Yoo and D. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces, Internat. J. Math. Math. Sci. 17 (1994), no. 2, 239-247. crossref(new window)

18.
I. Yoo and D. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces. II, J. Korean Math. Soc. 31 (1994), no. 1, 115-129.

19.
I. Yoo, T. S. Song, and B. S. Kim, A change of scale formula for Wiener integrals of unbounded functions. II, Commun. Korean Math. Soc. 21 (2006), no. 1, 117-133. crossref(new window)

20.
I. Yoo, T. S. Song, B. S. Kim, and K. S. Chang, A change of scale formula for Wiener integrals of unbounded functions, Rocky Mountain J. Math. 34 (2004), no. 1, 371-389. crossref(new window)

21.
I. Yoo and G. J. Yoon, Change of scale formulas for Yeh-Wiener integrals, Commun. Korean Math. Soc. 6 (1991), no. 1, 19-26.