CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2008-14

August 2008 (Revised January 2009)

The index theorem of regular variation and its applications

N. H. Bingham and A. J. Ostaszewski

We develop further the topological theory of regular variation of BOst13. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group T acting on a homogenous space X), thereby unifying and extending the multivariate regular variation literature. Here, working with real- time topological ows on homogeneous spaces, we identify an index of regular variation, which in a normed-vector space context may be specied using the Riesz representation theorem, and in a locally compact group setting may be connected with Haar measure.

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