A duality proof of sampling localisation in relaxation spectrum recovery

Loy, R. J., Newbury, C. M., Anderssen, R. S. and Davies, Arthur Russell 2001. A duality proof of sampling localisation in relaxation spectrum recovery. Bulletin of the Australian Mathematical Society 64 , pp. 265-269.

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Abstract

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

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
ISSN:	0004-9727
Last Modified:	04 Jun 2017 01:41
URI:	https://orca.cardiff.ac.uk/id/eprint/1713

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