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A Property of completely monotonic functions

Part of: Integral transforms, operational calculus

Published online by Cambridge University Press:  09 April 2009

Colm O'Cinneide
Colm O'Cinneide
Affiliation:
Statistics Division Department of Mathematical SciencesUniversity of ArkansasFayetteville, Arkansas 72701, U.S.A.
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Abstract

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A non-negative function f(t), t > 0, is said to be completely monotonic if its derivatives satisfy (-1)n fn (t) ≥ 0 for all t and n = 1, 2, …, For such a function, either f(t + δ) / f(t) is strictly increasing in t for each δ > 0, or f(t) = ce-dt for some constants c and d, and for all t. An application of this result is given.

MSC classification

Secondary: 44A10: Laplace transform
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 2 , April 1987 , pp. 143 - 146
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bakke, V. L. and Jackiewicz, Z., ‘Stability analysis of product θ-methods, for Abel integral equations of the second kind’, Numer. Math. 48 (1986), 127–136.CrossRefGoogle Scholar
[2]Phelps, R. R., Lectures on Choquet's Theorem (Van Nostrand Math. Studies, No. 7, Van Nostrand, New York, 1965).Google Scholar
[3]Ross, S. M., Stochastic Processes (John Wiley & Sons, New York, 1983).Google Scholar