2001年12月20日
Quasi-invariant measures on the group of diffeomorphisms and smooth vectors of unitary representations
Journal of Functional Analysis
- 巻
- 187
- 号
- 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.
- ID情報
-
- DOI : 10.1006/jfan.2001.3807
- ISSN : 0022-1236
- SCOPUS ID : 0035924684