Asymptotic behaviour of iterates of Volterra operators on Lp(0,1)
Abstract
We derive asymptotic information on the iterates of a Volterra convolution operator acting on Lp(0,1), subject to a mild smoothness condition on the kernel. In particular, an asymptotically equal sequence of rank 1 operators is obtained, leading to a simple asymptotic formula for the operator norms of the iterates.
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