Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE OPERATIONAL CALCULUS FOR A MEASURE-VALUED DYSON SERIES

  • Ryu, Kun-Sik (Department of Mathematics Han Nam University)
  • Published : 2006.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

Keywords

References

  1. R. H. Cameron and D. A. Storvick, An operator-valued function space integral and related integral equation, J. Math. Mech. 18 (1968), no. 16, 517-549
  2. R. P. Feynman, Space-time approach to non-relastivistic quantum mechanics, Revs. Modern Phys. 20 (1948), 367-387 https://doi.org/10.1103/RevModPhys.20.367
  3. R. P. Feynman, An operator calculus having applications in quantum electrodynamics, Physical Review 80 (1951), no. 1, 108-128 https://doi.org/10.1103/PhysRev.80.108
  4. G. W. Johnson and M. L. Lapidus, Noncommutative operations on Wiener functionals and Feynman's operational calculus, J. Funct. Anal. 81 (1988), no. 1, 74-99 https://doi.org/10.1016/0022-1236(88)90113-9
  5. K. S. Ryu and M. K. Im, A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula, Trans. Amer. Math. Soc. 354 (2002), no. 12, 4921-4951 https://doi.org/10.1090/S0002-9947-02-03077-5
  6. K. S. Ryu and M. K. Im, The measure-valued Dyson series and its stability theorems, J. Korean Math. Soc. (to appear)

Cited by

  1. THE ROTATION THEOREM ON ANALOGUE OF WIENER SPACE vol.29, pp.4, 2007, https://doi.org/10.5831/HMJ.2007.29.4.577
  2. Survey of the Theories for Analogue of Wiener Measure Space vol.15, pp.3, 2009, https://doi.org/10.4036/iis.2009.319