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Quantum stochastic evolutions

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Abstract

Quantum stochastic differential inclusions of hypermaximal monotone type are studied, under very general conditions, by means of certain discrete schemes which approximate them. The existence of an evolution operator corresponding to each such inclusion is proved.

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References

  • Aubin, J.-P., and Cellina, A. (1984).Differential Inclusions, Springer-Verlag, Berlin.

    Google Scholar 

  • Browder, F. E. (1976).Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, American Mathematical Society, Providence, Rhode Island.

    Google Scholar 

  • Crandall, M. G. (1973). A generalized domain for semigroup generations;Proceedings of the American Mathematical Society,37, 434–440.

    MATH  MathSciNet  Google Scholar 

  • Crandall, M. G., and Evans, L. C. (1975). On the relation of the operator ∂/∂τ+∂/∂s,Israel Journal of Mathematics,21, 261–278.

    MathSciNet  Google Scholar 

  • Crandall, M. G., and Pazy, A. (1972). Nonlinear evolution equations in Banach spaces,Israel Journal of Mathematics,11, 57–94.

    MathSciNet  Google Scholar 

  • Ekhaguere, G. O. S. (1992). Lipschizian quantum stochastic differential inclusions,International Journal of Theoretical Physics,31, 2003–2027.

    Article  MATH  MathSciNet  Google Scholar 

  • Ekhaguere, G. O. S. (1995). Quantum stochastic differential inclusions of hypermaximal monotone type,International Journal of Theoretical Physics,34, 323–353.

    Article  MATH  MathSciNet  Google Scholar 

  • Evans, L. C. (1977). Nonlinear evolution equations in an arbitrary Banach space,Israel Journal of Mathematics,26, 1–42.

    MATH  MathSciNet  Google Scholar 

  • Guichardet, A. (1972).Symmetric Hilbert Spaces and Related Topics, Springer-Verlag, Berlin.

    Google Scholar 

  • Hudson, R. L., and Parthasarathy, K. R. (1984). Quantum Ito's formula and stochastic evolutions,Communications in Mathematical Physics.93, 301–324.

    Article  MathSciNet  Google Scholar 

  • Iwamiya, T., Oharu, S., and Takahashi, T. (1986). On the class of nonlinear evolution operators in Banach space,Nonlinear Analysis,10, 315–337.

    Article  MathSciNet  Google Scholar 

  • Kisielewicz, M. (1991).Differential Inclusions and Optimal Control, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Kobayashi, Y. (1975). Difference approximation of evolution equations and generation of nonlinear semi-groups,Proceedings of the Japan Academy,51, 406–410.

    MATH  MathSciNet  Google Scholar 

  • Kobayasi, K., Kobayashi, Y., and Oharu, S. (1984). Nonlinear evolution operators in Banach spaces,Osaka Journal of Mathematics,21, 281–310.

    MathSciNet  Google Scholar 

  • Oharu, S. (1986). A class of nonlinear evolution operators: Basic properties and generation theory, inSemigroups, Theory and Applications, Vol. 1, H. Brezis, M. G. Crandall, and F. Kappel, eds., Longman Scientific and Technical, Essex.

    Google Scholar 

  • Reed, M., and Simon, B. (1972).Methods of Modern Mathematical Physics: I: Functional Analysis, Academic Press, New York.

    Google Scholar 

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Author notes

  1. G. O. S. Ekhaguere

    Present address: Department of Mathematics, University of Ibadan, Ibadan, Nigeria

Authors and Affiliations

  1. International Centre for Theoretical Physics, P.O. Box 586, I-34 100, Trieste, Italy

    G. O. S. Ekhaguere

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  1. G. O. S. Ekhaguere
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Ekhaguere, G.O.S. Quantum stochastic evolutions. Int J Theor Phys 35, 1909–1946 (1996). https://doi.org/10.1007/BF02302422

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  • DOI: https://doi.org/10.1007/BF02302422

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