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CONVERGENCE IN RELAXATION SPECTRUM RECOVERY
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 1 / February 2017
- Published online by Cambridge University Press:
- 02 November 2016, pp. 121-132
- Print publication:
- February 2017
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- Article
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Because of its practical and theoretical importance in rheology, numerous algorithms have been proposed and utilised to solve the convolution equation
$g(x)=(\text{sech}\,\star h)(x)\;(x\in \mathbb{R})$ for 
$h$ , given 
$g$ . There are several approaches involving the use of series expansions of derivatives of 
$g$ , which are then truncated to a small number of terms for practical application. Such truncations can only be expected to be valid if the infinite series converge. In this note, we examine two specific truncations and provide a rigorous analysis to obtain sufficient conditions on 
$g$ (and equivalently on 
$h$ ) for the convergence of the series concerned.
