DOI QR코드

DOI QR Code

SOME RELATIONSHIPS BETWEEN THE INTEGRAL TRANSFORM AND THE CONVOLUTION PRODUCT ON ABSTRACT WIENER SPACE

  • 투고 : 2014.11.18
  • 심사 : 2015.01.15
  • 발행 : 2015.01.31

초록

In this paper we establish several formulas for multiple integral transform of functionals defined on abstract Wiener space. We then use the these results to establish several basic formulas involving multiple convolution products.

키워드

참고문헌

  1. 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
  2. S. J. Chang, H. S. Chung, and D. Skoug, Convolution products, integral transforms and inverse integral transforms of functionals in $L_2$($C_0$[0, T]), Integral Transforms Spec. Funct. 21 (2010), 143-151. https://doi.org/10.1080/10652460903063382
  3. S. J. Chang, D. Skoug and H. S. Chung, Relationships for modified generalized integral transform and modified convolution product on function space, Integral Transforms Spec. Funct. 25 (2014), 790-804. https://doi.org/10.1080/10652469.2014.918614
  4. H. S. Chung, D. Skoug, and S. J. Chang, A Fubini theorem for integral transforms and convolution products, Int. J. Math. 24 (2013), Article ID 1350024 (13 pages).
  5. K. S. Chang, B. S. Kim, and I. Yoo, Integral transforms and convolution of analytic functionals on abstract Wiener space, Numer. Funct. Anal. Optim. 21 (2000), 97-105. https://doi.org/10.1080/01630560008816942
  6. L. Gross, Abstract Wiener space, Proc. Fifth Berkeley Sympos. Math. Stat. Prob. 2 (1965), 31-42.
  7. M. K. Im, U. C. Ji, and Y. J. Park, Relations among 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
  8. 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
  9. H.-H. Kuo Gaussian Measures in Banach Spaces, Lecture Note in Mathematics, Springer, Berlin 463 (1980), 579-598.
  10. B.J. Kim, B.S. Kim and D. Skoug, Integral transforms, convolution products and first variations, Int. J. Math. Math. Soc. 11 (2004), 579-598.
  11. B.S. Kim and D. Skoug, Integral transforms of functionals in $L_2$($C_0$[0, T]), Rocky Mountain J. Math. 33 (2003), 1379-1393. https://doi.org/10.1216/rmjm/1181075469
  12. Y.J. Lee, Applications of the Fourier-Wiener transform to differential equations on infinite dimensional spaces I, Trans. Amer. Math. Soc. 262 (1980), 259-283.
  13. 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