Approximation of and by completely monotone functions

Rick J. Loy; Robert Scott Anderssen

doi:10.21914/anziamj.v61i0.14757

Authors

Rick J. Loy Australian National University
Robert Scott Anderssen CSIRO http://orcid.org/0000-0001-8344-2346

DOI:

https://doi.org/10.21914/anziamj.v61i0.14757

Keywords:

complete and absolute monotonicity, stretched exponential, approximation, completely monotone and Kohlrausch functions, uniform and pointwise convergence.

Abstract

We investigate convergence in the cone of completely monotone fu nctions. Particular attention is paid to the approximation of and by exponentials and stretched exponentials. The need for such an analysis is a consequence of the fact that although stretched exponentials can be approximated by sums of exponentials, exponentials cannot in general be approximated by sums of stretched exponentials. doi:10.1017/S1446181120000012

Author Biographies

Rick J. Loy, Australian National University

Mathematical Sciences Institute, Hanna Neumann Building No. 145, Australian National University, Canberra, ACT 2601, Australia.

Robert Scott Anderssen, CSIRO

Data61, CSIRO, GPO Box 1700, Canberra, ACT 2601, Australia.