Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T02:37:39.563Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Class of Metrical Automorphisms on Gaussian Measure Space

Published online by Cambridge University Press:  22 January 2016

Hisao Nomoto
Hisao Nomoto*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let E be an infinite dimensional real nuclear space and H be its completion by a continuous Hilbertian norm ║ ║ of E. Then we have the relation

where E* is the conjugate space of E. Consider a function C(ξ) on E defined by the formula

(1)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 21 - 25
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Gelfand, I.M. and Vilenkin, N.Ya., Generalized functions, IV, New York, Academic Press, 1964.Google Scholar
[2] Hida, T. and Ikeda, N., Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles, University of California Press, 1965, Vol. 2. 117–143.Google Scholar
[3] Hida, T., Kubo, I., Nomoto, H. and Yoshizawa, H., On projective invariance of Brownian motion, Publ. Res. Inst. Math. Sci. (in press).Google Scholar
[4] von Neumann, J., Einige Sätze über messbare Abbildungen, Ann. Math., 33 (1932), 574–586.Google Scholar
[5] von Neumann, J., Zur Operatorenmethode in der klassischen Mechanik, Ann. Math., 33 (1932), 587–642.Google Scholar
[6] Prohorov, Yu.V., The method of charachteristic functionals, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles, University of California Press, 1961, Vol. 2, 403–419.Google Scholar