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A REVISED DUALITY PROOF OF SAMPLING LOCALIZATION IN RELAXATION SPECTRUM RECOVERY

Part of: Foundations, constitutive equations, rheology Integral equations, integral transforms Distributions, generalized functions, distribution spaces

Published online by Cambridge University Press:  09 February 2009

R. J. LOY ,
A. R. DAVIES  and
R. S. ANDERSSEN
R. J. LOY
Affiliation:
Department of Mathematics, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia (email: [email protected])
A. R. DAVIES
Affiliation:
School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, Wales, UK (email: [email protected])
R. S. ANDERSSEN*
Affiliation:
CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra ACT 2601, Australia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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The duality proof of sampling localization given by Loy, Newbury, Anderssen and Davies in 2001 contains an oversight, as the classes of functions chosen do not assume the compact support. Here, it is shown how a minor change to the argument there yields a precise conclusion.

Keywords

relaxation spectrum recoverysampling localizationregularizationduality

MSC classification

Secondary: 76A05: Non-Newtonian fluids 46F12: Integral transforms in distribution spaces 65R32: Inverse problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 79 - 83
Copyright
Copyright © Australian Mathematical Society 2009

References

[1] Davies, A. R. and Anderssen, R. S., ‘Sampling localization in determining the relaxation spectra’, J. Non-Newt. Fluid Mech. 73 (1997), 163–179.CrossRefGoogle Scholar
[2] Davies, A. R. and Anderssen, R. S., ‘Sampling localization and duality algorithms in practice’, J. Non-Newt. Fluid Mech. 79 (1998), 235–253.CrossRefGoogle Scholar
[3] Dienstfrey, A. and Greengard, L., ‘Analytic continuation, singular-value expansions, and Kramers–Kronig analysis’, Inverse Problems 17 (2001), 1307–1320.CrossRefGoogle Scholar
[4] Lavrentév, M. M., Some Improperly Posed Problems of Mathematical Physics, Springer Tracts in Nat. Philos., II (Springer, New York, 1967).CrossRefGoogle Scholar
[5] Loy, R. J., Newbury, C., Anderssen, R. S. and Davies, A. R., ‘A duality proof of sampling localization in relaxation spectrum recovery’, Bull. Aust. Math. Soc. 64 (2001), 265–269.CrossRefGoogle Scholar
[6] Macdonald, J. R., ‘On relaxation-spectrum estimation for decades of data: accuracy and sampling localization considerations’, Inverse Problems 16 (2000), 1561–1583.CrossRefGoogle Scholar
[7] Renardy, M., ‘On the use of Laplace transform inversion for reconstruction of relaxation spectra’, J. Non-Newt. Fluid Mech. 154 (2008), 47–51. Available online atwww.sciencedirect.com/science/journal/03770257CrossRefGoogle Scholar