New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem
We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the behavior of their restriction on N0. We give a complete answer t...
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Published in | Arab journal of mathematical sciences Vol. 25; no. 1; pp. 57 - 82 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.01.2019
Emerald Publishing |
Subjects | |
Online Access | Get full text |
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Summary: | We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the behavior of their restriction on N0. We give a complete answer to the following question: Can we affirm that a functionfis completely monotone (resp. a Bernstein function) if we know that the sequencef(k)kis completely monotone (resp. alternating)? This approach constitutes a kind of converse to Hausdorff’s moment characterization theorem in the context of completely monotone sequences. |
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ISSN: | 1319-5166 |
DOI: | 10.1016/j.ajmsc.2018.03.001 |