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Norms of Iterates of Volterra Operators on L^2

Eveson, S. (2003) Norms of Iterates of Volterra Operators on L^2. Journal of Operator Theory, 50 (2). pp. 369-386. ISSN 1841-7744

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It has recently been established that if V is the classical Volterra (indefinite integration) operator acting on the Hilbert space L2([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.

Item Type: Article
Keywords: Volterra operators
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 14 May 2009 15:50
Last Modified: 14 May 2009 15:50
Status: Published
Publisher: The Theta Foundation
URI: http://eprints.whiterose.ac.uk/id/eprint/7662

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