Commutative Wick algebras I. The Bargmann, Wiener and Fock algebras

  • W. Słowikowski
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 644)


Hilbert Space Scalar Product Base Space Linear Span Gaussian Measure 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. Bargmann, On Hilbert space of analytic functions and an associated integral transform, Pure Appl. Math. 14 (1961), 187–214. Remarks on a Hilbert space of analytic functions, Proc. Nat. Acad. Sci. USA 48 (1942), 199–204.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    K. Ito, Multiple Wiener integral, J. Math. Soc. Japan 3 (1951), 157–169. Complex multiple Wiener integral, Japan J. Math. 22 (1952), 63–86.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    G. Kallianpur, The role of reproducing Kernel Hilbert spaces in the study of Gaussian processes, Advances in Prob. and Related Topics 2 (1970), 49–83.MathSciNetzbMATHGoogle Scholar
  4. 4.
    E. Nelson, The free Markow field, J. Funct. Anal. 12 (1973), 211–227.CrossRefzbMATHGoogle Scholar
  5. 5.
    B. Simon, The P(φ)2 Euclidean (quantum) field theory, Princeton University Press, 1947Google Scholar
  6. 6.
    W. Słowikowski, The second quantization, the stochastic integration and measures in linear spaces, Mat. Inst. Aarhus Univ., Preprint Series No. 5, 1976/77Google Scholar
  7. 7.
    W. Słowikowski, Commutative Wick algebras. II Square integrable martingale algebras and Ito algebras, Proceedings to the Conference on Measure Theory — Applications to Stochastic Filtering and Control, Math. Forschungsinst. Oberwolfach, July 1977. To appear in Springer Lecture Notes Series.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • W. Słowikowski
    • 1
  1. 1.Institute of MathematicsUniversity of AarhusAarhusDenmark

Personalised recommendations