A note on deconvolution with completely monotone sequences and discrete fractional calculus
Publication
, Journal Article
Li, L; Liu, JG
Published in: Quarterly of Applied Mathematics
January 1, 2018
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,..), and show the consistency with time-continuous Riemann-Liouville calculus, which may be suitable for modeling memory kernels in discrete time series.
Duke Scholars
Published In
Quarterly of Applied Mathematics
DOI
EISSN
1552-4485
ISSN
0033-569X
Publication Date
January 1, 2018
Volume
76
Issue
1
Start / End Page
189 / 198
Related Subject Headings
- Applied Mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Li, L., & Liu, J. G. (2018). A note on deconvolution with completely monotone sequences and discrete fractional calculus. Quarterly of Applied Mathematics, 76(1), 189–198. https://doi.org/10.1090/qam/1479
Li, L., and J. G. Liu. “A note on deconvolution with completely monotone sequences and discrete fractional calculus.” Quarterly of Applied Mathematics 76, no. 1 (January 1, 2018): 189–98. https://doi.org/10.1090/qam/1479.
Li L, Liu JG. A note on deconvolution with completely monotone sequences and discrete fractional calculus. Quarterly of Applied Mathematics. 2018 Jan 1;76(1):189–98.
Li, L., and J. G. Liu. “A note on deconvolution with completely monotone sequences and discrete fractional calculus.” Quarterly of Applied Mathematics, vol. 76, no. 1, Jan. 2018, pp. 189–98. Scopus, doi:10.1090/qam/1479.
Li L, Liu JG. A note on deconvolution with completely monotone sequences and discrete fractional calculus. Quarterly of Applied Mathematics. 2018 Jan 1;76(1):189–198.
Published In
Quarterly of Applied Mathematics
DOI
EISSN
1552-4485
ISSN
0033-569X
Publication Date
January 1, 2018
Volume
76
Issue
1
Start / End Page
189 / 198
Related Subject Headings
- Applied Mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics