Abstract
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.
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H. Airault et P. Malliavin. Intégration géométrique sur l’espace de Wiener, Bull. Se. Math., 112, 1988, 3–52.
M.P. Malliavinet P. Malliavin. Quasi invariant integration on loop group, J. of Funct. Analysis, 1990, 93, 207–236.
M.P. Malliavinet P. Malliavin. Mesures quasi invariantes sur certains groupes de dimension infinie, Note aux C.R. Acad. Sc. Paris, octobre 1990.
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© 1991 Springer-Verlag Tokyo
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Malliavin, M.P., Malliavin, P. (1991). An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle. In: Kashiwara, M., Miwa, T. (eds) ICM-90 Satellite Conference Proceedings. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68170-0_12
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DOI: https://doi.org/10.1007/978-4-431-68170-0_12
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