Complete monotonicity and bernstein properties of functions are characterized by their restriction on N

Rafik Aguech; Wissem Jedidi

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arXiv · 1511.08345

Complete monotonicity and bernstein properties of functions are characterized by their restriction on N

Rafik Aguech·Wissem Jedidi

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Abstract

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 the set of non-negative integers. We give a complete answer to the following question: Can we affirm that a function is completely monotone (resp. a Bernstein function) if we know that the sequence formed by its restriction on the integers is completely monotone (resp. alternating)? This approach constitutes a kind of converse of Hausdorff's moment characterization theorem in the context of completely monotone sequences.

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Rafik Aguech, Wissem Jedidi. 2015-11-26. Complete monotonicity and bernstein properties of functions are characterized by their restriction on N. https://arxiv.org/abs/1511.08345

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