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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Bibliographic Details
Published inArab journal of mathematical sciences Vol. 25; no. 1; pp. 57 - 82
Main Authors Aguech, Rafik, Jedidi, Wissem
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2019
Emerald Publishing
Subjects
Bernstein functions
Completely alternating functions
Completely alternating sequences
Completely monotone functions
Completely monotone sequences
Hausdorff moment problem
Hausdorff moment sequences
Self-decomposability
Self-decomposability
30E05
60B10
Hausdorff moment sequences
Completely alternating sequences
Completely monotone sequences
44A60
44A10
47A57
Hausdorff moment problem
Completely monotone functions
Completely alternating functions
Bernstein functions
60E07
60E05
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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.
ISSN:1319-5166
DOI:10.1016/j.ajmsc.2018.03.001