References
Berezin, F.A.: The Method of Second Quantization. New York: Academic Press 1966
Gross, L.: Potential theory on Hilbert space. J. Funct. Anal.1, 123–181 (1967)
Hida, T.: Analysis of Brownian Functionals. (Carleton-Ottawa Math. Lect. Note Ser., vol. 13) Ottawa: Carleton University 1975
Hida, T.: Brownian Motion. New York Heidelberg Berlin: Springer 1980
Hida, T., Kuo, H.-H., Obata, N.: Transformations for white noise functionals. J. Funct. Anal. (to appear)
Hida, T., Kuo, H.-H., Potthoff, J., Streit, L.: White Noise: An Infinite Dimensional Calculus. Monogr. (in preparation)
Hida, T., Obata, N., Saitô, K.: Infinite dimensional rotations and Laplacians in terms of white noise calculus. (Preprint 1991)
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
Huang, Z.-Y.: Quantum white noises—White noise approach to quantum stochastic calculus. (Preprint 1991)
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
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
Kuo, H.-H., Obata, N., Saitô, K.: Lévy Laplacian of generalized functions on a nuclear space. J. Funct. Anal.94, 74–92 (1990)
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
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
Obata, N.: A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups. Nagoya Math. J.118, 111–132 (1990)
Umemura, Y. (Yamasaki): On the infinite dimensional Laplacian operator. J. Math. Kyoto Univ.4, 477–492 (1965)
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
Author information
Authors and Affiliations
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
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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02571783