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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Manuscripta Mathematica.
( Vol. 98 NO.3 / (1999))
Courants Invariants Par Une Action Propre
Abdelhak Abouqateb,
Pages. 349-362
Abstract The purpose of this paper is to characterise the invariant sections-distributions by a proper action. More
precisely, we show that if $G$ is a connected Lie group acting on a differentiable vector bundle $E
ightarrow V$ such that
the induced action on $V$ is proper, then the topological vector space $(C^infty_c(E))'_G$ of the $G$-invariant linear
functionals (on the space $C^infty_c(E)$ of $C^infty$ sections with compact support) equipped with the induced weak-topology
(resp. the strong-topology), is isomorphic to the weak (resp. strong) topological dual of the space $overline{C}^infty_G(E)$
(of all $G$-invariant sections $sigma$ with compact quotient supp($sigma)/G)$ equipped with a suitable topology; this coincides
with the usual $C^infty$-topology if the orbit space is compact, and with the Schwartz-topology if the group $G$ is compact.
Contents 1. Introduction
2. Preliminaires
3. Demonstration du theoreme 2
3.1 Soit $\sigma \in C^\infty_c(V)$
3.2 Soit $\tau \in C^\infty_c(E)$
4. Demonstration du theoreme 1
Key words
Mathmatical Subject Classification 58A25, 58E40