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A duality proof of sampling localisation in relaxation spectrum recovery

Published online by Cambridge University Press:  17 April 2009

R. J. Loy ,
C. Newbury ,
R. S. Anderssen  and
A. R. Davies
R. J. Loy
Affiliation:
Department of Mathematics, School of Mathematical Sciences, Australian National University ACT 0200, Australia
C. Newbury
Affiliation:
Mathematical and Information Sciences, CSIRO, GPO Box 664, Canberra ACT 2601, Australia
R. S. Anderssen
Affiliation:
Institute for Non-Newtonian Fluid Mechanics, Department of Mathematics, University of Wales, Aberystwyth SY23 3BZ, United Kingdom
A. R. Davies
Affiliation:
Institute for Non-Newtonian Fluid Mechanics, Department of Mathematics, University of Wales, Aberystwyth SY23 3BZ, United Kingdom
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In a recent paper, Davies and Anderssen (1997) examined the range of relaxation times, on which the linear viscoelasticity relaxation spectrum could be reconstructed, when the oscillatory shear data were only known on a fixed finite interval of frequencies. In particular, they showed that, for such oscillatory shear data, knowledge about the relaxation spectrum could only be recovered on a specific finite interval of relaxation times. They referred to this phenomenon as sampling localisation. The purpose of this note is show how their result can be proved using a duality argument, and, thereby, establish the fundamental nature of sampling localisation in relaxation spectrum recovery.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 265 - 269
Copyright
Copyright © Australian Mathematical Society 2001

References

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