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http://dx.doi.org/10.4134/CKMS.2009.24.3.397

TRANSFORMS AND CONVOLUTIONS ON FUNCTION SPACE  

Chang, Seung-Jun (DEPARTMENT OF MATHEMATICS DANKOOK UNIVERSITY)
Choi, Jae-Gil (DEPARTMENT OF MATHEMATICS DANKOOK UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.24, no.3, 2009 , pp. 397-413 More about this Journal
Abstract
In this paper, for functionals of a generalized Brownian motion process, we show that the generalized Fourier-Feynman transform of the convolution product is a product of multiple transforms and that the conditional generalized Fourier-Feynman transform of the conditional convolution product is a product of multiple conditional transforms. This allows us to compute the (conditional) transform of the (conditional) convolution product without computing the (conditional) convolution product.
Keywords
generalized Brownian motion process; generalized Fourier-Feynman transform; convolution product; conditional generalized Fourier-Feynman transform; conditional convolution product;
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1 S. J. Chang and D. Skoug, Generalized Fourier-Feynman transforms and a first variation on function space, Integral Transforms Spec. Funct. 14 (2003), 375–393   DOI   ScienceOn
2 T. Huffman, C. Park, and D. Skoug, Generalized transforms and convolutions, Internat. J. Math. Math. Sci. 20 (1997), 19–32
3 C. Park and D. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), 381–394
4 M. D. Brue, A functional transform for Feynman integrals similar to the Fourier transform, Thesis, Univ. of Minnesota, Minneapolis, 1972
5 R. H. Cameron and D. A. Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1–30   DOI
6 T. Huffman, C. Park, and D. Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), 661–673
7 S. J. Chang, J. G. Choi, and D. Skoug, Evaluation formulas for conditional function space integrals I, Stoch. Anal. Appl. 25 (2007), 141–168   DOI   ScienceOn
8 S. J. Chang, J. G. Choi, and D. Skoug, Simple formulas for conditional function space integrals and applications, Integration: Mathematical Theory and Applications 1 (2008), 1–20
9 S. J. Chang and D. M. Chung, Conditional function space integrals with applications, Rocky Mountain J. Math. 26 (1996), 37–62   DOI   ScienceOn
10 T. Huffman, C. Park, and D. Skoug, Convolution and Fourier-Feynman transforms of functionals involving multiple integrals, Michigan Math. J. 43 (1996), 247–261   DOI
11 T. Huffman, C. Park, and D. Skoug, Convolution and Fourier-Feynman transforms, Rocky Mountain J. Math. 27 (1997), 827–841
12 G. W. Johnson and D. L. Skoug, An Lp analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), 103–127
13 H.-H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math., no. 463, Springer, Berlin, 1975
14 C. Park and D. Skoug, Conditional Fourier-Feynman transforms and conditional convolution products, J. Korean Math. Soc. 38 (2001), 61–76   과학기술학회마을
15 J. Yeh, Stochastic Processes and the Wiener Integral, Marcel Dekker, Inc., New York, 1973
16 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), 2925–2948
17 J. Yeh, Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increment, Illinois J. Math. 15 (1971), 37–46