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AN ABSTRACT BOREL DENSITY THEOREM

By Martin Moskowttz

Abstract

Abstract. In this paper an abstract form of the Borel density theorem and related results is given centering around the notion of the author's of a (finite dimensional) "admissible " representation. A representation p is strongly admissible if each A'p is admissible. Although this notion is somewhat technical it is satisfied for certain pairs (G, p); e.g., if G is minimally almost periodic and p arbitrary, if G is complex analytic and p holomorphic. If G is real analytic with radical R, G/R has no compact factors and R acts under p with real eigenvalues, then p is strongly admissible. If in addition G is algebraic/R, then each R-rational representation is admissible. The results are proven in three stages where V is defined either over R or C. If p is a strongly admissible representation of G on V, then each (/-invariant measure fi on §(K), the Grassmann space of V, has support contained in the G-fixed point set. If p is a strongly admissible representation of G on V and G / H has finit

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.4071
Provided by: CiteSeerX
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