Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A note on deconvolution with completely monotone sequences and discrete fractional calculus

Authors: Lei Li and Jian-Guo Liu
Journal: Quart. Appl. Math. 76 (2018), 189-198
MSC (2010): Primary 47D03
DOI: https://doi.org/10.1090/qam/1479
Published electronically: August 22, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study in this work convolution groups generated by completely monotone sequences related to the ubiquitous time-delay 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,\ldots )$, and show the consistency with time-continuous Riemann-Liouville calculus, which may be suitable for modeling memory kernels in discrete time series.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2010): 47D03

Retrieve articles in all journals with MSC (2010): 47D03

Additional Information

Lei Li
Affiliation: Department of Mathematics, Duke University, Durham, NC 27708
Email: leili@math.duke.edu

Jian-Guo Liu
Affiliation: Departments of Physics and Mathematics, Duke University, Durham, NC 27708
Email: jliu@phy.duke.edu

DOI: https://doi.org/10.1090/qam/1479
Keywords: Convolution group, convolution inverse, completely monotone sequence, fractional calculus, Riemann-Liouville derivative.
Received by editor(s): July 3, 2017
Published electronically: August 22, 2017
Article copyright: © Copyright 2017 Brown University