Skip to main content
Log in

Rotation-invariant operators on white noise functionals

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Berezin, F.A.: The Method of Second Quantization. New York: Academic Press 1966

    MATH  Google Scholar 

  2. Gross, L.: Potential theory on Hilbert space. J. Funct. Anal.1, 123–181 (1967)

    Article  MATH  Google Scholar 

  3. Hida, T.: Analysis of Brownian Functionals. (Carleton-Ottawa Math. Lect. Note Ser., vol. 13) Ottawa: Carleton University 1975

    MATH  Google Scholar 

  4. Hida, T.: Brownian Motion. New York Heidelberg Berlin: Springer 1980

    MATH  Google Scholar 

  5. Hida, T., Kuo, H.-H., Obata, N.: Transformations for white noise functionals. J. Funct. Anal. (to appear)

  6. Hida, T., Kuo, H.-H., Potthoff, J., Streit, L.: White Noise: An Infinite Dimensional Calculus. Monogr. (in preparation)

  7. Hida, T., Obata, N., Saitô, K.: Infinite dimensional rotations and Laplacians in terms of white noise calculus. (Preprint 1991)

  8. Hida, T., Potthoff, J.: White noise analysis—An overview. In: Hida, T. et al. (eds.) White Noise Analysis, pp. 140–165. Singapore New Jersey London Hong Kong: World Scientific 1990

    Google Scholar 

  9. Huang, Z.-Y.: Quantum white noises—White noise approach to quantum stochastic calculus. (Preprint 1991)

  10. Krée, P.: La théorie des distributions en dimension quelconque et l'intégration stochastique. In: Korezlioglu, H., Ustunel, A.S. (eds.) Stochastic Analysis and Related Topics. Lect. Notes Math., vol. 1316, pp. 170–233. Berlin Heidelberg New York: Springer 1988

    Chapter  Google Scholar 

  11. Kuo, H.-H.: On Laplacian operators of generalized Brownian functionals. In: Itô, K., Hida, T. (eds.) Stochastic Processes and Their Applications. (Lect. Notes Math., vol. 1203, pp. 119–128) New York Heidelberg Berlin: Springer 1986

    Chapter  Google Scholar 

  12. Kuo, H.-H., Obata, N., Saitô, K.: Lévy Laplacian of generalized functions on a nuclear space. J. Funct. Anal.94, 74–92 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  13. Meyer, P.A.: Eléments de Probabilités quantiques IV. In: Azéma, J., Yor, M. (eds.) Séminaire de Probabilités XX. (Lect. Notes Math., vol. 1204, pp. 249–285) Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  14. Meyer, P.A.: Distributions noyaux, symboles d'après Krée. In: Azéma, J. et al. (eds.) Séminaire de Probabilités XXII. (Lect. Notes Math., vol. 1321, pp. 467–476) Berlin Heidelberg New York: Springer 1988

    Chapter  Google Scholar 

  15. Obata, N.: A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups. Nagoya Math. J.118, 111–132 (1990)

    MATH  MathSciNet  Google Scholar 

  16. Umemura, Y. (Yamasaki): On the infinite dimensional Laplacian operator. J. Math. Kyoto Univ.4, 477–492 (1965)

    MATH  MathSciNet  Google Scholar 

  17. Yoshizawa, H.: Rotation group of Hilbert space and its application to Brownian motion. In: Proc. International Conference on Functional Analysis and Related Topics, pp. 414–423. Tokyo: University of Tokyo Press 1970

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Professor T. Hida on the occasion of his retirement from Nagoya University

Supported by the Alexander von Humboldt-Stiftung

Rights and permissions

Reprints and permissions

About this article

Cite this article

Obata, N. Rotation-invariant operators on white noise functionals. Math Z 210, 69–89 (1992). https://doi.org/10.1007/BF02571783

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571783

Keywords

Navigation