MISC

2001年12月20日

Quasi-invariant measures on the group of diffeomorphisms and smooth vectors of unitary representations

Journal of Functional Analysis
  • Hiroaki Shimomura

187
2
開始ページ
406
終了ページ
441
記述言語
英語
掲載種別
DOI
10.1006/jfan.2001.3807
出版者・発行元
Academic Press Inc.

Let M be a smooth manifold and Diff0(M) the group of all smooth diffeomorphisms 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∞-vectors for a given unitary representation U of Diff0*(M), the connected component of the identity in Diff0(M). We first generalize some results of Shavgulidze on quasi-invariant measures on diffeomorphism groups. Then we prove the following result: Suppose that M is compact and U has the property that the action extends continuously to Diff*k(M), the group of Ck 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. © 2001 Elsevier Science.

リンク情報
DOI
https://doi.org/10.1006/jfan.2001.3807

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