Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

CALCULATION OF FUNCTIONS ON DISENTANGLING VIA MEASURES

  • Park, Yeon Hee (Department of Mathematics Education, Chonbuk National University) ;
  • Kim, Byoung Soo (School of Liberal Arts, Seoul National University of Science and Technology)
  • Received : 2018.05.11
  • Accepted : 2018.06.30
  • Published : 2018.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this note we give some results of the disentangling algebras and disentangling maps and calculate functions on disentangling via measures.

Keywords

References

  1. R. Feynman, An operator calculus having applications in quantum electrodynamics, Phys. Rev. 84 (1951), 108-128. https://doi.org/10.1103/PhysRev.84.108
  2. B. Jefferies and G.W. Johnson, Feynman's operational calculi for noncommuting operators: Definitions and elementary properties, Russian J. Math. Physics 8 (2001), 153-178.
  3. B. Jefferies and G.W. Johnson, Feynman's operational calculi for noncommuting operators: Tensors, ordered supports and disentangling an exponential factor, Math. Notes 70 (2001), 744-764. (Translated from Matematicheskie Zametki, vol. 70, no. 6, 2001, 815-838.) https://doi.org/10.1023/A:1012903732597
  4. B. Jefferies, G.W. Johnson and B.S. Kim, Feynman's operational calculi: methods for iterative disentangling, Acta Appl. Math. 92 (2006), 293-309. https://doi.org/10.1007/s10440-006-9061-2
  5. B. Jefferies, G.W. Johnson and L. Nielsen, Feynman's operational calculi for time dependent noncommuting operators, Proc. of the Seoul Conf. on the Feynman integral and related topics (July, 1999), J. Korean Math. Soc. 38 (2001), 193-226.
  6. G.W. Johnson and B.S. Kim, Extracting linear and bilinear factors in Feynman's operational calculi, Math. Phys. Anal. Geom. 6 (2003), 181-200. https://doi.org/10.1023/A:1024049113118
  7. G.W. Johnson and B.S. Kim, Derivational derivatives and Feynman's operational calculi, Houston J. Math. 35 (2009), 647-664.
  8. G.W. Johnson and M.L. Lapidus, The Feynman Integral and Feynman's Operational Calculus, Oxford U. Press, Oxford Mathematical Monograph, 2000. (Oxford U. Press paperback, 2002.)
  9. G.W. Johnson and M.L. Lapidus and Lance Nielsen, Feynman's Operational Calculus and Beyond, Oxford U. Press (2015).
  10. V.P. Maslov, Operational Methods, Mir, Moscow, 1976.
  11. V.E. Nazaikinskii, V.E. Shatalov and B.Yu. Sternin, Methods of Noncommutative Analysis, Walter de Gruyter, Studies in Math. 22, Berlin/New York, 1996.
  12. L. Nielsen, Effects of absolute continuity in Feynman's operational calculi, Proc. Amer. Math. Soc. 131 (2003), 781-791. https://doi.org/10.1090/S0002-9939-02-06592-9