CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2008-13

August 2008

Topological regular variation: III. Regular variation

N. H. Bingham and A. J. Ostaszewski

This paper extends the topological theory of regular variation of the slowly varying case of BOst13 to the regularly varying functions between metric groups, viewed as normed groups (see also BOst14). This employs the language of topological dynamics, especially flows and cocycles. In particular we show that regularly varying functions obey the chain rule and in the non-commutative context we characterize pairs of regularly varying functions whose product is regularly varying. The latter requires the use of a `differential modulus' akin to the modulus of Haar integration.

A PDF file (187 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2008-13, together with your name and postal address to:
CDAM Research Reports Series
Centre for Discrete and Applicable Mathematics
London School of Economics
Houghton Street
London WC2A 2AE, U.K.
Phone: +44(0)-20-7955 7494.
Fax: +44(0)-20-7955 6877.

Introduction to the CDAM Research Report Series.
CDAM Homepage.

Copyright © London School of Economics & Political Science 2007