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Affinely Prime Dynamical Systems(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)

Affinely Prime Dynamical Systems(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)
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摘要 This paper deals with representations of groups by "affine" automorphisms of compact, convex spaces, with special focus on "irreducible" representations: equivalently"minimal" actions. When the group in question is P SL(2, R), the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations. This analysis shows that, surprisingly, all these representations are equivalent. In fact, it is found that all irreducible affine representations of this group are equivalent. The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces. If it holds for the "universal strongly proximal space"of the group(to be defined), then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2017年第2期413-424,共12页 数学年刊(B辑英文版)
关键词 Irreducible affine dynamical systems Affinely prime Strong proximality Mbius transformations Harmonic functions Irreducible atone dynamical systems, Atfinely prime, Strong proximality,MSbius transformations, Harmonic functions
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