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http://dx.doi.org/10.11568/kjm.2014.22.1.57

PARTS FORMULAS INVOLVING CONDITIONAL INTEGRAL TRANSFORMS ON FUNCTION SPACE  

Kim, Bong Jin (Department of Mathematics Daejin University)
Kim, Byoung Soo (School of Liberal Arts Seoul National University of Science and Technology)
Publication Information
Korean Journal of Mathematics / v.22, no.1, 2014 , pp. 57-69 More about this Journal
Abstract
We obtain a formula for the conditional Wiener integral of the first variation of functionals and establish several integration by parts formulas of conditional Wiener integrals of functionals on a function space. We then apply these results to obtain various integration by parts formulas involving conditional integral transforms and conditional convolution products on the function space.
Keywords
conditional Wiener integral; conditional integral transform; conditional convolution; first variation;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 J.Yeh, Convolution in Fourier-Wiener transform, Pacific J. Math. 15 (1965), 731-738.   DOI
2 J.Yeh, Inversion of conditional Wiener integral, Pacific J. Math. 59 (1975), 623-638.   DOI
3 R.H.Cameron, The first variation of an indefinite Wiener integral, Proc. Amer. Math. Soc. 2 (1951), 914-924.   DOI   ScienceOn
4 R.H.Cameron and W.T.Martin, Fourier-Wiener transforms of analytic functionals, Duke Math. J. 12 (1945), 489-507.   DOI
5 R.H.Cameron and D.A.Storvick, A translation theorem for analytic Feynman integrals, Trans. Amer. Math. Soc. 125 (1966), 1-6.   DOI   ScienceOn
6 T.Huffman, C.Park and D.Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), 661-673.   DOI   ScienceOn
7 R.H.Cameron and D.A.Storvick, Feynman integral of variations of functionals, Gaussian Random Fields (Nagoya, 1990), Ser. Probab. Statist. 1, World Sci. Publ. 1991, 144-157.
8 S.J.Chang and D.Skoug, Parts formulas involving conditional Feynman integrals, Bull. Austral. Math. Soc. 65 (2002), 353-369.   DOI
9 B.J.Kim, B.S.Kim and D.Skoug, Conditional integral transforms, conditional convolution products and first variations, PanAmerican Math. J. 14 (2004), 27-47.
10 B.J.Kim and B.S.Kim, Parts formulas involving integral transforms on function space, Commun. Korean Math. Soc. 22 (2007), 553-564.   DOI   ScienceOn
11 B.J.Kim, B.S.Kim and D.Skoug, Integral transforms, convolution products and first variations, Internat. J. Math. Math. Sci. 2004 (2004), 579-598   DOI
12 Y.J.Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), 153-164.   DOI
13 C.Park, D.Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), 381-394.   DOI
14 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.   DOI   ScienceOn
15 D.Skoug and D.Storvick, A survey of results involving transforms and convolutions in function space, Rocky Mountain J. Math. 34 (2004), 1147-1175.   DOI   ScienceOn
16 R.H.Cameron and D.A.Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1-30.   DOI