On factorization representations for Avakumović--Karamata functions with nondegenerate groups of regular points

Author: Buldygin V. V.   Klesov O. I.   Steinebach J. G.  

Publisher: Springer Publishing Company

ISSN: 0133-3852

Source: Analysis Mathematica, Vol.30, Iss.3, 2004-01, pp. : 161-192

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

Avakumović-Karamata functions f are generalized regularly varying functions (so--called ORV functions) such that f*(&lgr;)= limsup x →∞f(&lgr;x)/f(x) is finite for all &lgr;>0. In this paper, we investigate classes of ORV functions with "nondegenerate groups of regular points", that is, having points &lgr;≥1, for which f*(&lgr;) exists as a positive and finite limit (instead of limsup) on a nontrivial subgroup of the positive real axis. Certain factorization representations, characterizations and uniform convergence theorems are proved, describing both the structure of ORV functions f as well as that of their limit functions f*. Some well-known results from regular variation theory are covered by this general approach.