The Index Theorem of topological regular variation and its applications

We develop further the topological theory of regular variation of [N.H. Bingham, A.J. Ostaszewski, Topological regular variation: I. Slow variation, LSE-CDAM-2008-11]. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group T acting on a h...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-10, Vol.358 (2), p.238-248
Main Authors: Bingham, N.H., Ostaszewski, A.J.
Format: Article
Language:English
Subjects:
Cocycles
Exact sciences and technology
Flows
Functional analysis
General topology
Global analysis, analysis on manifolds
Group theory
Mathematical analysis
Mathematics
Multivariate regular variation
Representation theorems
Sciences and techniques of general use
Topological dynamics
Topological groups, lie groups
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Uniform convergence theorem
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Summary:We develop further the topological theory of regular variation of [N.H. Bingham, A.J. Ostaszewski, Topological regular variation: I. Slow variation, LSE-CDAM-2008-11]. 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 flows on homogeneous spaces, we identify an index of regular variation, which in a normed-vector space context may be specified using the Riesz representation theorem, and in a locally compact group setting may be connected with Haar measure.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.03.071