Korean Journal of Mathematics

  • 제22권1호
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  • Pages.57-69
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  • 2014
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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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)
  • 투고 : 2013.11.06
  • 심사 : 2014.03.05
  • 발행 : 2014.03.30
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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.

키워드

참고문헌

  1. R.H.Cameron, The first variation of an indefinite Wiener integral, Proc. Amer. Math. Soc. 2 (1951), 914-924. https://doi.org/10.1090/S0002-9939-1951-0045937-X
  2. 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
  3. R.H.Cameron and D.A.Storvick, A translation theorem for analytic Feynman integrals, Trans. Amer. Math. Soc. 125 (1966), 1-6. https://doi.org/10.1090/S0002-9947-1966-0200987-0
  4. R.H.Cameron and D.A.Storvick, An $L_2$ analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1-30. https://doi.org/10.1307/mmj/1029001617
  5. 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.
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  7. T.Huffman, C.Park and D.Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), 661-673. https://doi.org/10.1090/S0002-9947-1995-1242088-7
  8. B.J.Kim and B.S.Kim, Parts formulas involving integral transforms on function space, Commun. Korean Math. Soc. 22 (2007), 553-564. https://doi.org/10.4134/CKMS.2007.22.4.553
  9. 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 https://doi.org/10.1155/S0161171204305260
  10. 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.
  11. Y.J.Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), 153-164. https://doi.org/10.1016/0022-1236(82)90103-3
  12. C.Park, D.Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), 381-394. https://doi.org/10.2140/pjm.1988.135.381
  13. 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. https://doi.org/10.1216/rmjm/1181071725
  14. D.Skoug and D.Storvick, A survey of results involving transforms and convolutions in function space, Rocky Mountain J. Math. 34 (2004), 1147-1175. https://doi.org/10.1216/rmjm/1181069848
  15. J.Yeh, Convolution in Fourier-Wiener transform, Pacific J. Math. 15 (1965), 731-738. https://doi.org/10.2140/pjm.1965.15.731
  16. J.Yeh, Inversion of conditional Wiener integral, Pacific J. Math. 59 (1975), 623-638. https://doi.org/10.2140/pjm.1975.59.623

피인용 문헌

  1. Generalized Cameron–Storvick theorem and its applications vol.29, pp.1, 2018, https://doi.org/10.1080/10652469.2017.1346636
  2. GENERALIZED CAMERON-STORVICK TYPE THEOREM VIA THE BOUNDED LINEAR OPERATORS vol.57, pp.3, 2014, https://doi.org/10.4134/jkms.j190276
  3. Some Relationships for the Generalized Integral Transform on Function Space vol.8, pp.12, 2014, https://doi.org/10.3390/math8122246