Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T15:41:05.899Z Has data issue: false hasContentIssue false
  • English
  • Français

A REVISED DUALITY PROOF OF SAMPLING LOCALIZATION IN RELAXATION SPECTRUM RECOVERY

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

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: rick.loy@maths.anu.edu.au)
A. R. DAVIES
Affiliation:
School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, Wales, UK (email: daviesr@cardiff.ac.uk)
R. S. ANDERSSEN*
Affiliation:
CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra ACT 2601, Australia (email: bob.anderssen@csiro.au)
*
✉For correspondence; e-mail: bob.anderssen@csiro.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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