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


Journal Article

© 2017 Brown University. 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.

Full Text

Duke Authors

Cited Authors

  • Li, L; Liu, JG

Published Date

  • January 1, 2018

Published In

Volume / Issue

  • 76 / 1

Start / End Page

  • 189 - 198

Electronic International Standard Serial Number (EISSN)

  • 1552-4485

International Standard Serial Number (ISSN)

  • 0033-569X

Digital Object Identifier (DOI)

  • 10.1090/qam/1479

Citation Source

  • Scopus