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PARTS FORMULAS INVOLVING CONDITIONAL INTEGRAL TRANSFORMS ON FUNCTION SPACE

김병수|김봉진
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2014.03|한국수학논문집 (Korean Journal of Mathematics)|제22권 제1호|pp. 57-69|DOI http://dx.doi.org/10.11568/kjm.2014.22.1.57

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참고문헌

키워드

first variationconditional Wiener integralconditional integral transformconditional convolution
주제분류수학

초록

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.

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.

참고문헌 (16)

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  4. R.H.Cameron, "An L2L2 analytic Fourier-Feynman transform", Michigan Math. J, 23, pp.1~30 (1976)
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  7. T.Huffman, "Analytic Fourier-Feynman transforms and convolution", Trans. Amer. Math. Soc, 347, pp.661~673 (1995)
  8. 김봉진, "Parts formulas involving integral transforms on function space", 대한수학회논문집, 22(4), pp.553~564 (2007), 대한수학회
  9. B.J.Kim, "Integral transforms, convolution products and first variations", J. Math. Math. Sci, 2004, pp.579~598 (2004)
  10. B.J.Kim, "Conditional integral transforms, conditional convolution products and first variations", PanAmerican Math. J, 14, pp.27~47 (2004)
  11. Y.J.Lee, "Integral transforms of analytic functions on abstract Wiener spaces", J. Funct. Anal, 47, pp.153~164 (1982)
  12. C.Park, "A simple formula for conditional Wiener integrals with applications", Pacific J. Math, 135, pp.381~394 (1988)
  13. C.Park, "Relationships among the first variation, the convolution product, and the Fourier-Feynman transform", Rocky Mountain J. Math, 28, pp.1447~1468 (1998)
  14. D.Skoug, "A survey of results involving transforms and convolutions in function space", Rocky Mountain J. Math, 34, pp.1147~1175 (2004)
  15. J.Yeh, "Convolution in Fourier-Wiener transform", Pacific J. Math, 15, pp.731~738 (1965)
  16. J.Yeh, "Inversion of conditional Wiener integral", Pacific J. Math, 59, pp.623~638 (1975)

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