DOI QR코드

DOI QR Code

RELATIONSHIPS AMONG FOURIER-YEH-FEYNMAN TRANSFORM, CONVOLUTION AND THE FIRST VARIATION ON YEH-WIENER SPACE

  • Kim, Bong-Jin (Department of Mathematics, Daejin University) ;
  • Kim, Byoung-Soo (School of Liberal Arts, Seoul National University of Science and Technology)
  • Received : 2011.03.17
  • Accepted : 2011.04.22
  • Published : 2011.06.25

Abstract

We examine the various relationships that exist among the Fourier-Yeh-Feynman transform, convolution and the first variation for functionals on Yeh-Wiener space that belong to a Banach algebra S(Q).

Keywords

Yeh-Wiener space;Fourier-Yeh-Feynman transform;convolution;first variation

References

  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. 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
  3. R.H. Cameron and D.A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, Analytic Functions (Kozubnik, 1979), Lecture Notes in Math. 798, Springer-Verlag, Berlin, 1980, 18-67.
  4. K.S. Chang, D.H. Cho, B.S. Kim, T.S. Song and I. Yoo, Relationships involving generalized Fourier-Feynman transform, convolution and first variation, Integral Transforms Spec. Funct. 16 (2005), 391-405. https://doi.org/10.1080/10652460412331320359
  5. K.S. Chang, B.S. Kim and I. Yoo, Fourier-Feynman transform, convolution and first variation of functionals on abstract Wiener space, Integral Transforms Spec. Funct. 10 (2000), 179-200. https://doi.org/10.1080/10652460008819285
  6. 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
  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/10.2307/2154908
  8. T. Hu man, 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
  9. G.W. Johnson and D.L. Skoug, An $L_p$ analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), 103-127. https://doi.org/10.1307/mmj/1029002166
  10. B.J. Kim, B.S. Kim and I. Yoo, Integral transforms of functionals on a function space of two variables, J. Chungcheong Math. Soc. 23 (2010), 349-362.
  11. B.S. Kim, Integral transforms of square integrable functionals on Yeh-Wiener space, Kyungpook Math. J. 49 (2009), 155-166. https://doi.org/10.5666/KMJ.2009.49.1.155
  12. B.S. Kim and Y.K. Yang, Fourier-Yeh-Feynman transform and convolution on Yeh-Wiener space, Korean J. Math. 16 (2008), 335-348.
  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, Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc. 95 (1960), 433-450. https://doi.org/10.1090/S0002-9947-1960-0125433-1
  16. J. Yeh, Stochastic processes and the Wiener integral, Marcel Dekker, New York, 1973.

Cited by

  1. FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FOURIER-TYPE FUNCTIONALS ON WIENER SPACE vol.29, pp.5, 2013, https://doi.org/10.7858/eamj.2013.031