Acknowledgement
Supported by : Dankook University
References
- R. H. Cameron, Some examples of Fourier-Wiener transforms of analytic functionals, Duke Math. J. 12 (1945), 485-488. https://doi.org/10.1215/S0012-7094-45-01243-9
- R. H. Cameron and W. T. Martin, Fourier-Wiener transforms of analytic functionals, Duke Math. J. 12 (1945), 489-507. https://doi.org/10.1215/S0012-7094-45-01244-0
-
R. H. Cameron and D. A. Storvick, Fourier-Wiener transforms of functionals belonging to
$L_2$ over the space C, Duke Math. J. 14 (1947), 99-107. https://doi.org/10.1215/S0012-7094-47-01409-9 - K. S. Chang, B. S. Kim, and I. Yoo, Integral transforms 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, 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, Convolution products, integral transforms and inverse integral transforms of functionals in
$L_2(C_0[0, T])$ , Integral Transforms Spec. Funct. 21 (2010), no. 1-2, 143-151. https://doi.org/10.1080/10652460903063382 - S. J. Chang, H. S. Chung, and D. Skoug, Some basic relationships among transforms, convolution products, first varia-tions and inverse transforms, Cent. Eur. J. Math. 11 (2013), no. 3, 538-551.
- H. S. Chung, J. G. Choi, and S. J. Chang, A Fubini theorem on a function space and its applications, Banach J. Math. Anal. 7 (2013), no. 1, 173-185. https://doi.org/10.15352/bjma/1358864557
- H. S. Chung, D. Skoug, and S. J. Chang, A Fubini theorem for integral transforms and convolution products, Internat. J. Math. 24 (2013), no. 3, Article ID 1350024, 13 pages.
- H. S. Chung, D. Skoug, and S. J. Chang, Relationships involving transforms and convolutions via the translation theorem, Stoch. Anal. Appl. 32 (2014), no. 2, 348-363. https://doi.org/10.1080/07362994.2013.877350
- 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
- U. C. Ji and N. Obata, Quantum white noise calculus, Non-commutativity, infinite-dimensionality and probability at the crossroads, 143-191, QP-PQ: Quantum Probab. White Noise Anal. 16, World Sci.Publ., River Edge, NJ, 2002.
- B. J. Kim, B. S. Kim, and D. Skoug, Integral transforms, convolution products and first variations, Int. J. Math. Math. Sci. 2004 (2004), no. 9-12, 579-598. https://doi.org/10.1155/S0161171204305260
-
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 - Y. J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), no. 2, 153-164. https://doi.org/10.1016/0022-1236(82)90103-3
-
Y. J. Lee, Unitary operators on the space of
$L^2$ -functions over abstract Wiener spaces, Soochow J. Math. 13 (1987), no. 2, 165-174. - E. Nelson, Dynamical Theories of Brownian Motion, 2nd edition, Math. Notes, Princeton University Press, Princeton, 1967.
- L. A. Shepp, Radon-Nikodym derivatives of Gaussian measures, Ann. Math. Statist. 37 (1966), 321-354. https://doi.org/10.1214/aoms/1177699516
- D. Skoug and D. Storvick, A survey of results involving transforms and convolutions in function space, Rocky Mountain J. Math. 34 (2004), no. 3, 1147-1175. https://doi.org/10.1216/rmjm/1181069848
- 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.
- J. Yeh, Stochastic Processes and the Wiener Integral, Marcel Dekker, Inc., New York, 1973.
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