Skip to main content

Convolution semigroups in quantum probability and quantum stochastic calculus

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

Keywords

  • Compact Group
  • Quantum Probability
  • Convolution Semigroup
  • Quantum Stochastic Calculus
  • Quantum Stochastic Differential Equation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    CrossRef  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).

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  MATH  Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  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).

    CrossRef  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).

    CrossRef  MathSciNet  Google Scholar 

  22. A. Frigerio, in pp. 207–222.

    CrossRef  Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51613-2

  • Online ISBN: 978-3-540-46713-7

  • eBook Packages: Springer Book Archive