On ergodic quasi-invariant measures on the circle group
β Scribed by V Mandrekar; M Nadkarni
- Publisher
- Elsevier Science
- Year
- 1969
- Tongue
- English
- Weight
- 395 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0022-1236
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π SIMILAR VOLUMES
Let M be a smooth manifold and Diff 0 (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
The convex set M a of quasi-invariant measures on a locally convex space E with given ``shift''-Radon Nikodym derivatives (i.e., cocycles) a=(a tk ) k # K 0 , t # R is analyzed. The extreme points of M a are characterized and proved to be non-empty. A specification (of lattice type) is constructed s
Integration by parts formulas are established both for Wiener measure on the path space of a loop group and for the heat kernel measures on the loop group. The Wiener measure is defined to be the law of a certain loop group valued ``Brownian motion'' and the heat kernel measures are time t, t>0, dis