<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Eveson, Simon</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Asymptotic Behaviour of Iterates of Volterra Operators on $L^p(0,1)$</style></title><secondary-title><style face="normal" font="default" size="100%">Integral Equations and Operator Theory</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Analysis</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.springerlink.com/content/x18h355x4602j342/</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Birkhäuser Basel</style></publisher><volume><style face="normal" font="default" size="100%">53</style></volume><pages><style face="normal" font="default" size="100%">331-341</style></pages><isbn><style face="normal" font="default" size="100%">ISSN 0378-620X</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Given k ? L1 (0,1) satisfying certain smoothness and growth conditions at 0, we consider the Volterra convolution operator Vk defined on Lp (0,1) by  
and its iterates We construct some much simpler sequences which, as n ? ?, are asymptotically equal in the operator norm to Vkn. This leads to a simple asymptotic formula for ||Vkn|| and to a simple ‘asymptotically extremal sequence’; that is, a sequence (un) in Lp (0, 1) with ||un||p=1 and as n ? ?. As an application, we derive a limit theorem for large deviations, which appears to be beyond the established theory. </style></abstract><custom1><style face="normal" font="default" size="100%">arXiv:math/0409516v1</style></custom1></record></records></xml>