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Some general properties of the liouville operator

  • Quantum Theory Beyond Hilbert Space
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Irreversibility and Causality Semigroups and Rigged Hilbert Spaces

Part of the book series: Lecture Notes in Physics ((LNP,volume 504-504))

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References

  1. E.P. Wigner, Ann. Math. 40, 149 (1939).

    Article  MathSciNet  Google Scholar 

  2. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol I: Functional Analysis, Academic Press, New York 1980.

    Google Scholar 

  3. E. E. Prugovecki Quantum Mechanics in Hilbert Space, Academic Press, New York 1981.

    MATH  Google Scholar 

  4. I. Prigogine Non-Equilibrium Statistical Mechanics, Wiley, New York 1962.

    MATH  Google Scholar 

  5. A. Bohm, Boulder Lectures in Theoretical Physics, vol 19A, 255 (1965).

    Google Scholar 

  6. A. Bohm, Quantum Mechanics. Foundations and Applications. Springer Verlag, Berlin (1994).

    Google Scholar 

  7. A. Bohm and M. Gadella, Dirac Kets, Gamow Vectors and Gel'fand Triplets., Lecture Notes in Physics, vol 348, Berlin (1989).

    Google Scholar 

  8. M. Reed and B. Simon, Methods of Modern Mathematical Physics Vol II: Fourier Analysis. Self Adjointness, Academic Press, New York 1975.

    Google Scholar 

  9. B. Pavlov, Russ. Math. Sur., 42, 127 (1987). See also reference 7.

    Article  MATH  Google Scholar 

  10. H. Weidmann Linear Operators in Hilbert space, Springer Verlag 1980.

    Google Scholar 

  11. H. Spohn, The spectrum of the Liouville-von Neumann operator, J. Math Phys. 17 57–60 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Bellisard Schroedinger Operators with Almost Periodic Potential: an Overview Lecture Notes in Physics 153, 356–363 (1982).

    Article  Google Scholar 

  13. H. Steinhaus A new property of the Cantor set (in Polish), Wektor 7, (1917), 1–3 English translation: H. Steinhaus Selected Papers, PWN Warsaw 1985.

    Google Scholar 

  14. P. Billingsley Probability and measure, Wiley, New York 1985.

    Google Scholar 

  15. I. Antoniou, S.A. Shkarin, Z. Suchanecki Spectrum of the Hamiltonian and spectrum of the Liouvillian, Preprint 1997.

    Google Scholar 

  16. N. Levenberg, Jr., G.J. Martin, A.L. Shields and S. Zdravkovska, Factorizations of Lebesgue measure via convolution, Proc. Amer. Math. Soc. 104 419–430 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  17. L. Bas, B.S. Pavlov Absolute Continuity of Convolution of Singular Measures and Localization Problems ULB Preprint (1995)

    Google Scholar 

  18. K. Falconer Fractal geometry: mathematical foundations and applications, Chichester, Wiley 1990.

    MATH  Google Scholar 

  19. N. Wiener and A. Wintner, Fourier-Stieltjes transforms and singular infinite convolution, Amer. J. Math. 60 513–522 (1938).

    Article  MATH  MathSciNet  Google Scholar 

  20. P. Erdös, On a family of symmetric Bernoulli convolutions, Amer. J. Math 61 974–976 (1939).

    Article  MathSciNet  Google Scholar 

  21. I.M. Gel'fand and G.P. Shilov, Generalized Functions, vol. 4, Academic Press, New York (1964).

    Google Scholar 

  22. K. Maurin Generalized Eigenfunction Expansions and Unitary Representations of Topological Groups, Polish Scientific Publishers, Warsawa (1968).

    Google Scholar 

  23. H.H. Schaeffer, Topological Vector Spaces, Springer Verlag, Berlin (1970).

    Google Scholar 

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Arno Bohm Heinz-Dietrich Doebner Piotr Kielanowski

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© 1998 Springer-Verlag

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Antoniou, I., Gadella, M., Suchanecki, Z. (1998). Some general properties of the liouville operator. In: Bohm, A., Doebner, HD., Kielanowski, P. (eds) Irreversibility and Causality Semigroups and Rigged Hilbert Spaces. Lecture Notes in Physics, vol 504-504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106775

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  • DOI: https://doi.org/10.1007/BFb0106775

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  • Print ISBN: 978-3-540-64305-0

  • Online ISBN: 978-3-540-69725-1

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