- ACADEMIC PRESS INC ELSEVIER SCIENCE
Let M be a smooth manifold and Diff(0)(M) the group of all smooth diffeomorphisnis on M with compact support. Our main subject in this paper concerns the existence of certain quasi-invariant measures on groups of diffeomorphisms, and the denseness of C-infinity-vectors for a given unitary representation U of Diff(0)*,(M), the connected component of the identity in Diff(0)(M). We first generalize some results of Shavgulidze on quasi-invariant measures on diffeomorphisin groups. Then we prove the following result: Suppose that H is compact and 17 has the property that the action extends continuously to Diff**(M), the group of C-k diffeomorphisms which are homotopic to the identity, for some finite k. Then U has a dense set of C-vectors. We also give an extension of our theorem to non-compact M. (C) 2001 Elsevier Science.
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