DOI QR코드

DOI QR Code

FURTHER RESULTS INVOLVING THE HILBERT SPACE L2a,b[0, T]

  • Choi, Jae Gil (School of General Education, Dankook University) ;
  • Skoug, David (Department of Mathematics, University of Nebraska-Lincoln)
  • Received : 2018.10.28
  • Accepted : 2020.01.26
  • Published : 2020.02.29

Abstract

In this paper we determine conditions which a function a(t) must satisfy to insure that the function a'(t) is an element of the separable Hilbert space L2a,b[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.

Keywords

References

  1. R.H. Cameron & W.T. Martin: Transformations of Wiener integrals under translations. Ann. of Math. 45 (1944), no. 2, 386-396. https://doi.org/10.2307/1969276
  2. S.J. Chang, J.G. Choi & D. Skoug: A generalized Fourier-Feynman transform on the product function space $C_{a,b}$[0, T] and related topics. arXiv:1309.7176 (2013).
  3. S.J. Chang & D.M. Chung: Conditional function space integrals with applications. Rocky Mountain J. Math. 26 (1996), 37-62. https://doi.org/10.1216/rmjm/1181072102
  4. S.J. Chang, H.S. Chung & D. Skoug: Integral transforms of functionals in $L_2$($C_{a,b}$[0, T]). J. Fourier Anal. Appl. 15 (2009), 441-462. https://doi.org/10.1007/s00041-009-9076-y
  5. S.J. Chang, H.S. Chung & D. Skoug: Some basic relationships among transforms, convolution products, first variation, and inverse transforms. Cent. Eur. J. Math. 11 (2013), 538-551.
  6. S.J. Chang & D. Skoug: The effect of drift on conditional Fourier-Feynman transforms and conditional convolution products. Int. J. Appl. Math. 2 (2000), 505-527.
  7. S.J. Chang & D. Skoug: Generalized Fourier-Feynman transforms and a first variation on function space. Integral Transforms Spec. Funct. 14 (2003), 375-393. https://doi.org/10.1080/1065246031000074425
  8. I. Pierce & D. Skoug: Integration formulas for functionals on the function space $C_{a,b}$[0, T] involving Paley-Wiener-Zygmund stochastic integrals. Panamerican Math. J. 18 (2008), 101-112.
  9. J. Yeh: Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments. Illinois J. Math. 15 (1971), 37-46. https://doi.org/10.1215/ijm/1256052816
  10. J. Yeh: Stochastic Processes and the Wiener Integral. Marcel Dekker, Inc., New York, 1973.