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A duality proof of sampling localisation in relaxation spectrum recovery
Published online by Cambridge University Press: 17 April 2009
Extract
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
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