Approximation of and by completely monotone functions

Rick J. Loy, Robert Scott Anderssen

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

Keywords


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



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



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.