References
- R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45 (1944), 386-396. https://doi.org/10.2307/1969276
- R. H. Cameron and W. T. Martin, The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals, Ann. of Math. (2) 48 (1947), 385-392. https://doi.org/10.2307/1969178
- S. J. Chang and J. G. Choi, Translation theorem for function space integral associated with Gaussian paths and applications, to appear in the Bull. Iranian Math. Soc.
- 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. https://doi.org/10.1080/07362990601052185
- S. J. Chang and D. M. Chung, Conditional function space integrals with applications, Rocky Mountain J. Math. 26 (1996), no. 1, 37-62. https://doi.org/10.1216/rmjm/1181072102
- S. J. Chang and H. S. Chung, Some expressions for the inverse integral transform via the translation theorem on function space, J. Korean Math. Soc. 53 (2016), no. 6, 1261-1273. https://doi.org/10.4134/JKMS.j150485
-
S. J. Chang, H. S. Chung, and D. Skoug, Integral transforms of functionals in
$L^2(C_{a,b}[0,\;T])$ , J. Fourier Anal. Appl. 15 (2009), no. 4, 441-462. https://doi.org/10.1007/s00041-009-9076-y - S. J. Chang, H. S. Chung, and D. Skoug, Some basic relationships among transforms, convolution products, first variations and inverse transforms, Cent. Eur. J. Math. 11 (2013), no. 3, 538-551. https: //doi.org/10.2478/s11533-012-0148-x
- K. S. Chang, B. S. Kim, and I. Yoo, Integral transform and convolution of analytic functionals on abstract Wiener space, Numer. Funct. Anal. Optim. 21 (2000), no. 1-2, 97-105. https://doi.org/10.1080/01630560008816942
- 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. https://doi.org/10.1080/1065246031000074425
- S. J. Chang, D. Skoug, and H. S. Chung, Relationships for modified generalized integral transforms, modified convolution products and first variations on function space, Integral Transforms Spec. Funct. 25 (2014), no. 10, 790-804. https://doi.org/10.1080/10652469.2014.918614
- D. M. Chung and U. C. Ji, Transforms on white noise functionals with their applications to Cauchy problems, Nagoya Math. J. 147 (1997), 1-23. https://doi.org/10.1017/S0027763000006292
- H. S. Chung and V. K. Tuan, Generalized integral transforms and convolution products on function space, Integral Transforms Spec. Funct. 22 (2011), no. 8, 573-586. https: //doi.org/10.1080/10652469.2010.535798
- L. Gross, Abstract Wiener spaces, in Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 1, 31-42, Univ. California Press, Berkeley, CA, 1967.
- M. K. Im, U. C. Ji, and Y. J. Park, Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms, Bull. Korean Math. Soc. 48 (2011), no. 2, 291-302. https://doi.org/10.4134/BKMS.2011.48.2.291
- B. J. Kim, Conditional integral transforms, conditional convolution products and first variations for some conditioning functions, Far East J. Math. Sci. (FJMS) 19 (2005), no. 3, 245-258.
- B. J. Kim and B. S. Kim, Parts formulas involving conditional integral transforms on function space, Korea J. Math. 22 (2014), no. 1, 57-69. https://doi.org/10.11568/kjm.2014.22.1.57
- B. J. Kim, B. S. Kim, and D. Skoug, Conditional integral transforms, conditional convolution products and first variations, Pan Amer. Math. J. 14 (2004), no. 3, 27-47.
-
B. S. Kim and D. Skoug, Integral transforms of functionals in
$L_2$ ($C_0$ [0, T]), Rocky Mountain J. Math. 33 (2003), no. 4, 1379-1393. https://doi.org/10.1216/rmjm/1181075469 - H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Mathematics, Vol. 463, Springer-Verlag, Berlin, 1975.
- Y. J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Functional Analysis 47 (1982), no. 2, 153-164. https://doi.org/10.1016/0022-1236(82)90103-3
- E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, NJ, 1967.
- 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. http://projecteuclid.org/euclid.ijm/1256052816 https://doi.org/10.1215/ijm/1256052816
- J. Yeh, Stochastic Processes and the Wiener Integral, Marcel Dekker, #Inc., New York, 1973.