Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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NEW RESULTS ON STABILITY PROPERTIES FOR THE FEYNMAN INTEGRAL VIA ADDITIVE FUNCTIONALS

  • Lim, Jung-Ah (Department of Mathematics and Statistics University of Nebraska-Lincoln)
  • Published : 2002.07.01
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Abstract

It is known that the analytic operator-valued Feynman integral exists for some "potentials" which we so singular that they must be given by measures rather than by functions. Corresponding stability results involving monotonicity assumptions have been established by the author and others. Here in our main theorem we prove further stability theorem without monotonicity requirements.

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References

  1. Acta Appl. Math. v.42 The analytic operator-valued Feyrnman integral via additive functionals of Broqnian motion S. Albeverio;G. W. Johnson;Z. M. Ma https://doi.org/10.1007/BF01064169
  2. J. Funct. Anal. v.199 Perturbation of Dirichlet forms S. Albeverio;Z. M. Ma
  3. Stochastic processes, physocs and geometry Semigroup of Schrodinger operators with potentials given by Radon measures Blanchard;Z. M. Ma
  4. Lecture Notes in Math New results on the Schrodinger semigroups with potentials given by smooth measures Blanchard;Z. M. Ma
  5. Markov processes and potential theory R. M. Blumenthal;R. K. Getoor
  6. Rocky Mountain J. Math. v.29 Stability theorem for the Feynman integral via time continuation K. S. Chang;J. A. Lim;K. S. Ryu https://doi.org/10.1216/rmjm/1181070404
  7. Mathematical surveys no.15 Vector measures J. Diestel:J. J. Uhl
  8. Rev. Modern Phys. v.20 Space-time approach to non-relativistic quantum mechanics R. P. Feynman https://doi.org/10.1103/RevModPhys.20.367
  9. Dirichlet forms and Markov processes M. Fukushima
  10. Amer. Math. Soc. Colloq. Pub. v.31 Functional analysis and semi-groups E. Hille;R. S. Philips
  11. J. Math. Phys. v.25 A bounded convergence theorem for the Feynman integral G. W. Johnson https://doi.org/10.1063/1.526289
  12. Se minaire d;Anlyse Moderne 20 Existence theorems for the analytic operator-valued Feynman integral G. W. Johnson
  13. J. of Math. Phys. v.41 A dominated-type convergence theorem for the Feynman integral G. W. Johnson;J. G. Kim https://doi.org/10.1063/1.533294
  14. Mem. Amer. Math. Soc. v.62 no.351 Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman's operatinal calculus G. W. Johnson;M. L. Lapidus
  15. Oxford Mathematical Monographs The Feynman integral and Feynman's operational calculus G. W. Johnson
  16. Perturbation theory for linear operators(2nd ed.) T. Kato
  17. Integrals and operators(2nd rev. and enl. ed.) R. A. Kunze;I. E. Segal
  18. Integral Equations Operator Theory v.8 Perturbation theory and a dominated convergence theorem for Feynman integrals M. L. Lapidus https://doi.org/10.1007/BF01199981
  19. Commun. Korean Math. Soc. v.13 no.3 Stability theorem for the Feynman integral via additive functionals J. A. Lim
  20. An introduction to the theory of (non-symmetric) Dirichlet forms Z. M. Ma;M. Rockner
  21. Functional analysis v.I Methods of modern mathematical physics M. Reed;B. Simon
  22. Fourier analysis, Self-adjointness v.Ⅱ Methods of modern mathematical physics M. Reed;B. Simon
  23. J. Funct. Anal. v.28 A canonical decomposition for quadratic forms with applications to monotone convergence theorems B. Simon https://doi.org/10.1016/0022-1236(78)90094-0
  24. Bull. Amer. Math. Soc. v.7 Schrodinger semigroups B. Simon https://doi.org/10.1090/S0273-0979-1982-15041-8