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On the continuity of the Wiener-Hopf factorization operation

Published online by Cambridge University Press:  17 February 2009

Michael Green  and
Brian D.O. Anderson
Michael Green
Affiliation:
Department of Systems Engineering, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, Canberra, A.C.T., 2601, Australia.
Brian D.O. Anderson
Affiliation:
Department of Systems Engineering, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, Canberra, A.C.T., 2601, Australia.
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Abstract

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The problem of passing from an L∞ function to a Wiener-Hopf factorization is considered. It is shown that a small L∞ perturbation which does not change the factorization indices will lead to small Lp (1 < p < ∞) perturbations in the Wiener-Hopf factors, but can lead to large L∞ perturbations, unless the derivatives are controlled during the perturbation.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 4 , April 1987 , pp. 443 - 461
Copyright
Copyright © Australian Mathematical Society 1987

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