Skip to main content
SpringerLink
Log in

Dirichlet forms and generalized Schrödinger operators

  • Conference paper
  • First Online:
Schrödinger Operators

Part of the book series: Lecture Notes in Physics ((LNP,volume 345))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albeverio, S.: Some points of interaction between stochastic analysis and quantum theory, pp. 1–26 in “Stochastic differential systems”, Ed. N. Christopeit, K. Helmes, M. Kohlmann, Lect. Notes Control Inf. Sci. 78, Springer, Berlin (1986)

    Google Scholar 

  2. Albeverio, S.; Blanchard, Ph.; Høegh-Krohn, R.: Reduction of non linear problems to Schrödinger or heat equations: Formation of Kepler orbits, singular solutions for hydrodynamical equations, pp. 189–206 in “Stochastic Aspects of classical and quantum Systems”, Ed. S. Albeverio, Ph. Combe, M. Sirague-Collin, Lect. Notes Math. 1109, Springer, Berlin (1985)

    Google Scholar 

  3. Albeverio, S.; Fenstad, J. E.; Høegh-Krohn, R.; Lindström, T.: Non standard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, New York-San Francisco-London 1986

    Google Scholar 

  4. Albeverio, S.; Fukushima, M.; Karwowski, W.; Streit, L.: Capacity and quantum mechanical tunneling, Comm. Math. Phys. 81, 501–513 (1981)

    Google Scholar 

  5. Albeverio, S.; Gesztesy, F.; Høegh-Krohn, R.; Holden, H.: Solvable Models in Quantum Mechanics, Springer-Verlag: Berlin-Heidelberg-New York (1988)

    Google Scholar 

  6. Albeverio, S.; Gesztesy, F.; Karwowski, W.; Streit, L.: On the connection between Schrödinger and Dirichlet forms. J. Math. Phys. 26, 2546–2553 (1985)

    Google Scholar 

  7. Albeverio, S.; Høegh-Krohn, R.: Quasi-invariant measures, symmetric diffusion processes and quantum fields, in Les méthodes mathématiques de la théorie quantique des champs, Colloques Internationaux du C.N.R.S., No. 248, 23–27 Juin 1975, C.N.R.S. (1976)

    Google Scholar 

  8. Albeverio, S.; Høegh-Krohn, R.: Some remarks on Dirichlet forms and their application to quantum mechanics and statistical mechanics, pp. 120–132 in “Functional analysis in Markov processes, Ed. M. Fukushima, Lect. Notes Math. 923, Springer, Berlin (1982)

    Google Scholar 

  9. Albeverio, S.; Hida, T.; Potthoff, J.; Röckner, M.; Streit, L.: Dirichlet forms in terms of White noise analysis I, II in preparation

    Google Scholar 

  10. Albeverio, S.; Høegh-Krohn, R.; Streit, L.: Energy forms, Hamiltonians and distorted Brownian paths, J. Math. Phys. 18, 907–917 (1977)

    Google Scholar 

  11. Albeverio, S.; Høegh-Krohn, R.; Streit, L.: Regularization of Hamiltonians and processes, J. Math. Phys. 21, 1636–1642 (1980)

    Google Scholar 

  12. Albeverio, S.; Kusuoka, S.: Maximality of infinite dimensional Dirichlet forms and Høegh-Krohn 's model of quantum fields, Kyoto-Bochum Preprint (1988), to appear in Memorial Volume for R. Høegh-Krohn

    Google Scholar 

  13. Albeverio, S.; Kusuoka, S.; Röckner, M.: On partial integration in infinite dimensional space and applications to Dirichlet forms, Preprint Bochum 1988. Publication in preparation.

    Google Scholar 

  14. Albeverio, S.; Kusuoka, S.; Streit, L.: Convergence of Dirichlet forms and associated Schrödinger operators, J. Funct. Anal. 68, 130–148 (1986)

    Google Scholar 

  15. Albeverio, S.; Ma, Z.: Nowhere Radon smooth measures, perturbations of Dirichlet forms and singular quadratic forms, to appear in Proceedings Conference Bad Honnef 1988, Edts. N. Christopeit et al., Lect. Notes Information Control Springer, Berlin (1989)

    Google Scholar 

  16. Albeverio, S.; Röckner, M.: Classical Dirichlet forms on topological vector spaces — closability and a Cameron-Martin formula, to appear in: J. Funct. Anal.

    Google Scholar 

  17. Albeverio, S.; Röckner, M.: Classical Dirichlet forms on topological vector spaces-the construction of the associated diffusion process, Preprint Bochum 1988, to appear in Prob. Theory rel. fields

    Google Scholar 

  18. Albeverio, S.; Röckner, M.: On Dirichlet forms on topological vector spaces: existence and maximality, Preprint Bochum (1988), to appear in Proceedings Conference “Bad Honnef” 1988, Edts. N. Christopeit et al., Lect. Notes Information Control Springer, Berlin (1989)

    Google Scholar 

  19. Albeverio, S.; Räckner, M.: New developments in the theory and application of Dirichlet forms, to appear in Proceedings of the international conference in Ascona — Locarno on “Stochastic Processes, Physics and Geometry” edts. Albeverio, S.; Casati, G.; Cattaneo, U.; Merlini, D.; Moresi, R.; World Scientific Publishing Company, Singapore (1989)

    Google Scholar 

  20. Bauer, H.: Probability theory and elements of measure theory, de Gruyter: Berlin-New York (1981)

    Google Scholar 

  21. Bouleau, N.; Hida, T.: Formes de Dirichlet générales et densité des variables aléatoires réelles sur l'espace de Wiener, J. Funct. Anal. 69, 229–259 (1986)

    Google Scholar 

  22. Brasche, J. F.: Perturbations of self-adjoint operators supported by null sets. Dissertation zur Erlangung des Doktorgrades der Mathematik, Bielefeld (1988)

    Google Scholar 

  23. Brasche, J. F.: Dirichlet forms and generalized Schrödinger operators. To appear in Proceedings of the international conference in Dubna 1988 on “Schrödinger Operators — Standard and Non Standard”, edts. P. Exner, P. Seba, World Scientific Publishing Company, Singapore (1989)

    Google Scholar 

  24. Brasche, J. F.: An inverse problem in spectral analysis and the Efimov effect. To appear in Proceedings of the international conference in Ascona — Locarno on “Stochastic Processes, Physics and Geometry” edts. Albeverio, S.; Casati, G.; Cattaneo, U.; Merlini, D.; Moresi, R.; World Scientific Publishing Company, Singapore (1989)

    Google Scholar 

  25. Brasche, J. F.: Perturbations of Schroedinger Hamiltonians by measures-self-adjointness and lower semiboundedness, J. Math. Phys. 26, 621–626 (1985)

    Google Scholar 

  26. Davies, E. B.: One-parameter semigroups. London-New York-Toronto-Sydney-San Francisco: Academic Press (1980)

    Google Scholar 

  27. Elworthy, D.: Lectures et St. Flour, Warwick prepr. (1988)

    Google Scholar 

  28. Fukushima, M.: Dirichlet forms and Markov processes. North-Holland / Kodansha, Amsterdam-Oxford-New York (1980)

    Google Scholar 

  29. Fukushima, M.: Basic properties of Brownian motion and a capacity on the Wiener space, J. Math. Soc. Japan 36, 161–175

    Google Scholar 

  30. Fukushima, M.: Energy forms and diffusion processes, BiBoS-preprint 10 (1984)

    Google Scholar 

  31. Fukushima, M.: On a stochastic calculus related to Dirichlet forms and distorted Brownian motion, Physical Report 77, 255–262 (1981)

    Google Scholar 

  32. Gesztesy, F.: Some applications of commutative methods, these proceedings

    Google Scholar 

  33. Kato, T.: Perturbation Theory for linear Operators, Springer-Verlag, Berlin-Heidelberg-New York (1980)

    Google Scholar 

  34. Kondrat'ev, Ju. G.: Dirichlet operators and smoothness of the solutions of infinit-dimensional elliptic equations, Sov. Math. Dokt. 31, No. 3, 461–464 (1985)

    Google Scholar 

  35. Kondrat'ev, Ju. G.; Košmanenko, V. D: The scattering problem for operators associated with Dirichlet forms, Sov. Math. Dokt. 26, 585–589 (1982)

    Google Scholar 

  36. Kusuoka, S.: Dirichlet forms and diffusion processes on Banach space, J. Fac. Science Univ. Tokyo, Sec. 1A, 29, 79–95 (1982)

    Google Scholar 

  37. Maz'ja, V. G.; Havin, V. P.: Non-linear potential theory, Uspehi Mat Nauk 27, 67–138 (1972)

    Google Scholar 

  38. Oshima, Y.: Lectures on Dirichlet spaces, prepr., Erlangen (1988)

    Google Scholar 

  39. Pantic, D.: Stochastic calculus on the distorted Brownian motion, Belgrade prepr. (1986)

    Google Scholar 

  40. Reed, M.; Simon, B.:Modern mathematical physics, Vol. 14, Academic Press, New York-San Francisco-London, (1972, 1975, 1978, 1979)

    Google Scholar 

  41. Röckner, M.; Wielens, N.: Dirichlet forms — closability and change of speed measures, in Infinite dimensional Analysis and stochastic Processes, Editor: Albeverio, S., Boston-London-Melbourne: Pitman 1985

    Google Scholar 

  42. Rullkötter, K.; Spönemann, U.:Dirichletformen und Diffusionsprozesse, Diplomarbeit, Bielefeld (1983)

    Google Scholar 

  43. Silverstein, M. L.: Symmetric Markov processes, Lecture Notes in Math. 426, Springer-Verlag, Berlin-Heidelberg-New York (1974)

    Google Scholar 

  44. Silverstein, M. L.: Boundary theory for symmetric Markov processes, Lect. Notes in Math. 516, Springer, Berlin (1976)

    Google Scholar 

  45. Simon, B.: A canonical decomposition for quadratic forms with applications to monotone convergence theorems, J. Funct. Anal. 28, 377–385 (1978)

    Google Scholar 

  46. Spönemann, U.: Doctoral thesis in preparation, Bielefeld (1989)

    Google Scholar 

  47. Streit, L.: Quantum theory and stochastic processes — some contact points, pp. 197–213 in “Stochastic processes and their applications”, Edts. K. Ito, T. Hida, Lect. Notes Math. 1203, Springer, Berlin (1986)

    Google Scholar 

  48. Sturm, K. Th.: Störung von Hunt-Prozessen durch signierte additive Funktionale, Erlangen Dissertation (1989)

    Google Scholar 

  49. Takeda, M.: On the uniqueness of Markovian self-adjoint extensions of diffusion operators on infinite dimensional spaces, Osaka J. Math, 22, 733–742 (1985)

    Google Scholar 

  50. Wielens, N.; The essential self-adjointness of generalized Schrödinger operators, J. Funct. Anal. 61, 98–115 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität, D 4630, Bochum 1, Germany

    Sergio Alberio & Johannes Brasche

  2. BiBoS Research Centre, Bielefeld/Bochum, SFB 237, Bochum-Essen-Düsseldorf

    Sergio Alberio

  3. CERFIM, Locarno, Switzerland

    Sergio Alberio

  4. Department of Mathematics, University of Edingburgh, EH9 3JZ, Edingburgh, Scotland

    Michael Röckner

Authors
  1. Sergio Alberio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johannes Brasche
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Röckner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Helge Holden Arne Jensen

Additional information

Dedicated to the memory of Raphael Høegh-Krohn.

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Alberio, S., Brasche, J., Röckner, M. (1989). Dirichlet forms and generalized Schrödinger operators. In: Holden, H., Jensen, A. (eds) Schrödinger Operators. Lecture Notes in Physics, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51783-9_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-51783-9_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51783-2

  • Online ISBN: 978-3-540-46807-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation