An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle

  • Marie Paule Malliavin
  • Paul Malliavin
Conference paper


The group of difisomorphisms of a riemannian manifold of dimension >1 is very “ramified”. The existence of a “reasonnable” quasi invariant measure seems therefore very doubtfull. The case of the group of the diffeomorphisms of the circle S1 is quite different. We shall in this paper identify it with a loop space which carries a natural Wiener measure.


Central Extension Symmetric Operator Loop Space Left Action Wiener Space 
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    H. Airault et P. Malliavin. Intégration géométrique sur l’espace de Wiener, Bull. Se. Math., 112, 1988, 3–52.MathSciNetMATHGoogle Scholar
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    M.P. Malliavinet P. Malliavin. Quasi invariant integration on loop group, J. of Funct. Analysis, 1990, 93, 207–236.CrossRefGoogle Scholar
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    M.P. Malliavinet P. Malliavin. Mesures quasi invariantes sur certains groupes de dimension infinie, Note aux C.R. Acad. Sc. Paris, octobre 1990.Google Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Marie Paule Malliavin
    • 1
  • Paul Malliavin
    • 1
  1. 1.ParisFrance

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