Korean Journal of Mathematics

  • 제26권3호
  • /
  • Pages.387-403
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  • 2018
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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SHIFTING AND MODULATION FOR THE CONVOLUTION PRODUCT OF FUNCTIONALS IN A GENERALIZED FRESNEL CLASS

  • Kim, Byoung Soo (School of Liberal Arts Seoul National University of Science and Technology) ;
  • Park, Yeon Hee (Department of Mathematics Education Chonbuk National University)
  • 투고 : 2018.03.06
  • 심사 : 2018.07.20
  • 발행 : 2018.09.30
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초록

Shifting, scaling and modulation proprerties for the convolution product of the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal{F}}_{A1,A2}$ are given. These properties help us to obtain convolution product of new functionals from the convolution product of old functionals which we know their convolution product.

키워드

과제정보

연구 과제 주관 기관 : Seoul National University of Science and Technology

참고문헌

  1. J.M. Ahn, K.S. Chang, B.S. Kim and I. Yoo, Fourier-Feynman transform, convolution and first variation, Acta Math. Hungar. 100 (2003), 215-235. https://doi.org/10.1023/A:1025041525913
  2. S. Albeverio and R. Hoegh-Krohn, Mathematical theory of Feynman path integrals, Lecture Notes in Math. 523, Springer-Verlag, Berlin, 1976.
  3. R.H. Cameron and D.A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, in Analytic Functions (Kozubnik, 1979), Lecture Notes in Math. 798, Springer-Verlag, (1980), 18-67.
  4. K.S. Chang, B.S. Kim and I. Yoo, Analytic Fourier-Feynman transform and convolution of functionals on abstract Wiener space, Rocky Mountain J. Math. 30 (2000), 823-842. https://doi.org/10.1216/rmjm/1021477245
  5. 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
  6. T. Huffman, C. Park and D. Skoug, Convolutions and Fourier-Feynman transforms of functionals involving multiple integrals, Michigan Math. J. 43 (1996), 247-261. https://doi.org/10.1307/mmj/1029005461
  7. G.W. Johnson and D.L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), 157-176. https://doi.org/10.2140/pjm.1979.83.157
  8. G. Kallianpur and C. Bromley, Generalized Feynman integrals using analytic continuation in several complex variables, in "Stochastic Analysis and Application (ed. M.H.Pinsky)", Marcel-Dekker Inc., New York, 1984.
  9. G. Kallianpur, D. Kannan and R.L. Karandikar, Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces and a Cameron-Martin formula, Ann. Inst. Henri. Poincare 21 (1985), 323-361.
  10. B.S. Kim, Shifting and variational properties for Fourier-Feynman transform and convolution, J. Funct. Space. 2015 (2015), 1-9.
  11. B.S. Kim, Shifting and modulation for Fourier-Feynman transform of functionals in a generalized Fresnel class, Korean J. Math. 25 (2017), 335-247.
  12. B.S. Kim, T.S. Song and I.Yoo, Analytic Fourier-Feynman transform and convolution in a generalized Fresnel class, J. Chungcheong Math. Soc. 22 (2009), 481-495.
  13. P.V. O'Neil, Advanced engineering mathematics, 5th ed. Thomson (2003).
  14. I. Yoo, Convolution and the Fourier-Wiener transform on abstract Wiener space, Rocky Mountain J. Math. 25 (1995), 1577-1587. https://doi.org/10.1216/rmjm/1181072163
  15. I. Yoo and B.S. Kim, Fourier-Feynman transforms for functionals in a generalized Fresnel class, Commun. Korean Math. Soc. 22 (2007), 75-90. https://doi.org/10.4134/CKMS.2007.22.1.075