Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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YEH CONVOLUTION OF WHITE NOISE FUNCTIONALS

  • Ji, Un Cig (Department of Mathematics, Research institute of Mathematical Finance, Chungbuk National University) ;
  • Kim, Young Yi (Research institute for Natural Science, Hanyang University) ;
  • Park, Yoon Jung (Department of Mathematics, Chungbuk National University)
  • Received : 2013.03.19
  • Accepted : 2013.04.30
  • Published : 2013.09.30
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Abstract

In this paper, we study the Yeh convolution of white noise functionals. We first introduce the notion of Yeh convolution of test white noise functionals and prove a dual property of the Yeh convolution. By applying the dual object of the Yeh convolution, we study the Yeh convolution of generalized white noise functionals, which is a non-trivial extension. Finally, we study relations between the Yeh convolution and Fourier-Gauss, Fourier-Mehler transform.

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References

  1. D.M. Chung, T.S. Chung and U.C. Ji, A simple proof of analytic characterization theorem for operator symbols, Bull. Korean Math. Soc. 34 (1997), 421-436.
  2. D.M. Chung and U.C. Ji, Transforms groups on white noise functionals and their appli-cations, Appl. Math. Optim. 37 (1998), 205-223.
  3. L. Gross, Potential theory on Hilbert space, J. Funct. Anal. 1 (1967), 123-181. https://doi.org/10.1016/0022-1236(67)90030-4
  4. T. Hida, Analysis of Brownian Functionals, Carleton Math. Lect. Notes 3, 241-272.
  5. M.K. Im, U.C. Ji and Y.J. Park, Relations between the first variation, the convolutions and the generalized Fourier-Gauss transforms, Bull. Korean Math. Soc. 48 (2011), 291-302. https://doi.org/10.4134/BKMS.2011.48.2.291
  6. U.C. Ji and Y.Y. Kim, Convolution of white noise operators, Bull. Korean Math. Soc. 48 (2011), 1003-1014. https://doi.org/10.4134/BKMS.2011.48.5.1003
  7. U.C. Ji and N. Obata, A unified characterization theorem in white noise theory, Infin. Dim. Anal. Quantum Probab. Related Topics 6 (2003), 167-178. https://doi.org/10.1142/S0219025703001122
  8. H.-H. Kuo, White Noise Distribution Theory, CRC Press, 1996.
  9. H.-H. Kuo, J. Potthoff and L. Streit, A characterization of white noise test functionals, Nagoya Math. J. 121 (1991), 185-194. https://doi.org/10.1017/S0027763000003469
  10. 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
  11. N. Obata, An analytic characterization of symbols of operators on white noise functionals, J. Math. Soc. Japan 45 (1993), 421-445. https://doi.org/10.2969/jmsj/04530421
  12. N. Obata, White Noise Calculus and Fock Space, Lect. Notes on Math. 1577, Springer-Verlag, Berlin, 1994.
  13. J. Potthoff and L. Streit, A characterization of Hida distributions, J. Funct. Anal. 101 (1991), 212-229. https://doi.org/10.1016/0022-1236(91)90156-Y
  14. J. Yeh, Convolution in Fourier-Wiener transform, Pacific J. Math. 15 (1965), 731-738. https://doi.org/10.2140/pjm.1965.15.731

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