CDAM: Computational, Discrete and Applicable Mathematics@LSE |
|
CDAM Research Report, LSE-CDAM-2008-15August 2008 |
Regular variation, topological dynamics, and the Uniform Boundedness Theorem
A. J. Ostaszewski
In the metrizable topological groups context, a direct product construction (mimicking the `action groupoid') provides a multiplicative representation canonical for arbitrary continuous flows. This implies, modulo metric differences, the topological equivalence of the natural, flow setting of regular variation of BOst13 with the Bajanski and Karamata BajKar group formulation. In consequence topological theorems concerning subgroup actions may be lifted to the flow setting. Thus the Bajanski-Karamata Uniform Boundedness Theorem (UBT), as it applies to cocycles in the continuous and Baire cases, may be reformulated and refined to hold under Baire-style Carath$eacute;odory conditions. Its connection to the Banach-Steinhaus UBT is clarified. An application to Banach algebras is given.A PDF file (221 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-2008-15, 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. Email: info@maths.lse.ac.uk |
Introduction to the CDAM Research Report Series. | ||
CDAM Homepage. |