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Convolution semigroups in quantum probability and quantum stochastic calculus

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Quantum Probability and Applications IV

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1396))

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References

  1. E.B. Davies and J.T. Lewis, Commun. Math. Phys. 17, 239–260 (1970).

    Article  MathSciNet  Google Scholar 

  2. E.B. Davies, Quantum Theory of Open Systems (Academic, London, 1976).

    MATH  Google Scholar 

  3. A. Barchielli, Semesterbericht Funktionalanalysis, Tübingen, Sommersemester 1987, Band 12, 29–42 (1987).

    Google Scholar 

  4. A. Barchielli, Probability operators and convolution semigroups of instruments in quantum probability, preprint IFUM 334/FT (Milano, 1987).

    Google Scholar 

  5. A.S. Holevo, Conditionally positive definite functions and continuous measurement processes in quantum probability, preprint (Moscow, 1987).

    Google Scholar 

  6. E.B. Davies, Commun. Math. Phys. 15, 277–304 (1969); 19, 83–105 (1970); 22, 51–70 (1971).

    Article  Google Scholar 

  7. A. Barchielli, L. Lanz, and G.M. Prosperi, Found. Phys. 13, 779–812 (1983).

    Article  MathSciNet  Google Scholar 

  8. A. Barchielli, in "Stochastic Processes in Classical and Quantum Systems", edited by S. Albeverio, G. Casati, and D. Merlini, Lecture Notes in Physics, Vol. 262 (Springer, Berlin, 1986), pp. 14–23.

    Chapter  Google Scholar 

  9. A. Barchielli, J. Phys. A: Math. Gen. 20, 6341–6355 (1987).

    Article  MathSciNet  Google Scholar 

  10. A. Barchielli and G. Lupieri, J. Math. Phys. 26, 2222–2230 (1985).

    Article  MathSciNet  Google Scholar 

  11. A. Barchielli and G. Lupieri, in Quantum Probability and Applications II, ed. by L. Accardi and W. von Waldenfels, Lecture Notes in Mathematics, vol. 1136 (Springer, Berlin, 1985), pp. 57–66.

    Chapter  Google Scholar 

  12. K.R. Parthasarathy, Boll. U.M.I. 5-A, 391–397 (1986).

    Google Scholar 

  13. A.S. Holevo, in "Quantum Probability and Applications III," ed. by L. Accardi and W. von Waldenfels, Lecture Notes in Mathematics, vol. 1303 (Springer, Berlin, 1988), pp. 128–148.

    Chapter  Google Scholar 

  14. H. Heyer, Probability Measures on Locally Compact Groups (Springer, Berlin, 1977).

    Book  MATH  Google Scholar 

  15. R.L. Hudson and K.R. Parthasarathy, Commun. Math. Phys. 93, 301–323 (1984).

    Article  MathSciNet  Google Scholar 

  16. R.L. Hudson and K.R. Parthasarathy, Acta Appl. Math. 2, 353–378 (1984).

    Article  MathSciNet  Google Scholar 

  17. K.R. Parthasarathy and K.B. Sinha, in Ref. 13. pp. 232–250.

    Google Scholar 

  18. K.R. Parthasarathy and K. Schmidt, Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory, Lecture Notes in Mathematics, vol. 272 (Springer, Berlin, 1972).

    MATH  Google Scholar 

  19. M. Takesaki, Theory of Operator Algebras I (Springer, Berlin, 1979).

    Book  MATH  Google Scholar 

  20. J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien (Algèbres de von Neumann) (Gauthier-Villars, Paris, 1969).

    MATH  Google Scholar 

  21. A. Frigerio, Publ. R.I.M.S. Kyoto Univ. 21, 657–675 (1985).

    Article  MathSciNet  Google Scholar 

  22. A. Frigerio, in pp. 207–222.

    Chapter  Google Scholar 

  23. B. Russo and H.A. Dye, Duke Math. J. 33, 413–416 (1966).

    Article  MathSciNet  Google Scholar 

  24. H. Heyer, Dualität lokalcompakter Gruppen, Lecture Notes in Mathematics, vol. 150 (Springer, Berlin, 1970).

    Book  MATH  Google Scholar 

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Luigi Accardi Wilhelm von Waldenfels

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© 1989 Springer-Verlag

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Barchielli, A., Lupieri, G. (1989). Convolution semigroups in quantum probability and quantum stochastic calculus. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications IV. Lecture Notes in Mathematics, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083548

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  • DOI: https://doi.org/10.1007/BFb0083548

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  • Print ISBN: 978-3-540-51613-2

  • Online ISBN: 978-3-540-46713-7

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