<?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%">Norms of Iterates of Volterra Operators on $L^2$</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of 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%">2003</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.mathjournals.org/jot/2003-050-002/2003-050-002-010.pdf</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">THETA</style></publisher><volume><style face="normal" font="default" size="100%">50(2)</style></volume><pages><style face="normal" font="default" size="100%">369-386</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">It has recently been established that if $V$ is the classical Volterra (indefinite integration) operator acting on the Hilbert space $L^2([0,1])$, then the operator and Hilbert-Schmidt norms of $V^n$ are both asymptotically $1/(2n!)$. We extend this in two ways: firstly, we give a 
generalisation which applies to Volterra convolution operators with kernels satisfying a mild smoothness condition, and secondly we show that in the constant-kernel case the same asymptotic behaviour is shared by the trace norm, and hence by a wide class of operator norms.
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