Asymptotic Behaviour of Iterates of Volterra Operators on $L^p(0,1)$

Title	Asymptotic Behaviour of Iterates of Volterra Operators on $L^p(0,1)$
Publication Type	Journal Article
Year of Publication	2005
Authors	Eveson S
Journal	Integral Equations and Operator Theory
Volume	53
Pagination	331-341
Abstract	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.
URL	http://www.springerlink.com/content/x18h355x4602j342/
DOI	10.1007/s00020-003-1329-6
E-print number	arXiv:math/0409516v1

Department of Mathematics