MISC

2001年12月

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

JOURNAL OF FUNCTIONAL ANALYSIS
  • H 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 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.

Web of Science ® 被引用回数 : 11

リンク情報
DOI
https://doi.org/10.1006/jfan.2001.3807
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000173324100007&DestApp=WOS_CPL

エクスポート
BibTeX RIS