Math @ Duke

Publications [#333567] of JianGuo Liu
Papers Published
 Li, L; Liu, JG, A note on deconvolution with completely monotone sequences and discrete fractional calculus,
Quarterly of Applied Mathematics, vol. 76 no. 1
(January, 2018),
pp. 189198, American Mathematical Society (AMS) [doi]
(last updated on 2019/05/21)
Abstract: © 2017 Brown University. We study in this work convolution groups generated by completely monotone sequences related to the ubiquitous timedelay memory effect in physics and engineering. In the first part, we give an accurate description of the convolution inverse of a completely monotone sequence and show that the deconvolution with a completely monotone kernel is stable. In the second part, we study a discrete fractional calculus defined by the convolution group generated by the completely monotone sequence c (1) = (1, 1, 1,..), and show the consistency with timecontinuous RiemannLiouville calculus, which may be suitable for modeling memory kernels in discrete time series.


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