Cookies?
Library Header Image
LSE Research Online LSE Library Services

Regular variation, tological dynamics, and the uniform boundedness theorem

Ostaszewski, Adam (2010) Regular variation, tological dynamics, and the uniform boundedness theorem. Topology Proceedings, 36 . pp. 305-336. ISSN 0146-4124

Full text not available from this repository.

Abstract

In the metrizable topological groups context, a semi-direct product construction provides a canonical multiplicative representation for arbitrary continuous flows. This implies, modulo metric differences, the topological equivalence of the natural flow formalization of regular variation of N. H. Bingham and A. J. Ostaszewski in [Topological regular variation: I. Slow variation, [to appear in Topology and its Applications]with the B. Bajsanski and J. Karamata group formulation in [Regularly varying functions and the principle of egui-continuity, Publ. Ramanujan Inst. 1 (1968/1969), 235-246]. In consequence, topological theorems concerning subgroup actions may be lifted to the flow setting. Thus, the Bajsanski-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 Caratheodory conditions. Its connection to the classical UBT, due to Stefan Banach and Hugo Steinhaus, is clarified. An application to Banach algebras is given.

Item Type: Article
Official URL: http://topology.auburn.edu/tp/
Additional Information: © 2010 Topology Proceedings
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 10 Jun 2011 15:39
URL: http://eprints.lse.ac.uk/35910/

Actions (login required)

Record administration - authorised staff only Record administration - authorised staff only