New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem

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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Main Authors: Rafik Aguech, Wissem Jedidi
Format: Article
Language:English
Published: Emerald Publishing 2019-01-01
Series:Arab Journal of Mathematical Sciences
Online Access:http://www.sciencedirect.com/science/article/pii/S1319516618300288
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spelling doaj-bdadc368864f4b00a1a14a5ba78d2db42021-05-02T14:29:52ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662019-01-012515782New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theoremRafik Aguech0Wissem Jedidi1Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia; Université de Monastir, Faculté des Sciences de Monastir, Département de mathématiques, 5019 Monastir, TunisiaDepartment of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia; Université de Tunis El Manar, Faculté des Sciences de Tunis, LR11ES11 Laboratoire d’Analyse Mathématiques et Applications, 2092, Tunis, Tunisia; Corresponding author at: Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.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 function f is completely monotone (resp. a Bernstein function) if we know that the sequence f(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. Keywords: Completely monotone functions, Completely monotone sequences, Bernstein functions, Completely alternating functions, Completely alternating sequences, Hausdorff moment problem, Hausdorff moment sequences, Self-decomposability, 2010 Mathematics Subject Classification: 30E05, 44A10, 44A60, 47A57, 60E05, 60E07, 60B10http://www.sciencedirect.com/science/article/pii/S1319516618300288
collection DOAJ
language English
format Article
sources DOAJ
author Rafik Aguech
Wissem Jedidi
spellingShingle Rafik Aguech
Wissem Jedidi
New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem
Arab Journal of Mathematical Sciences
author_facet Rafik Aguech
Wissem Jedidi
author_sort Rafik Aguech
title New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem
title_short New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem
title_full New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem
title_fullStr New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem
title_full_unstemmed New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem
title_sort new characterizations of completely monotone functions and bernstein functions, a converse to hausdorff’s moment characterization theorem
publisher Emerald Publishing
series Arab Journal of Mathematical Sciences
issn 1319-5166
publishDate 2019-01-01
description 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 function f is completely monotone (resp. a Bernstein function) if we know that the sequence f(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. Keywords: Completely monotone functions, Completely monotone sequences, Bernstein functions, Completely alternating functions, Completely alternating sequences, Hausdorff moment problem, Hausdorff moment sequences, Self-decomposability, 2010 Mathematics Subject Classification: 30E05, 44A10, 44A60, 47A57, 60E05, 60E07, 60B10
url http://www.sciencedirect.com/science/article/pii/S1319516618300288
work_keys_str_mv AT rafikaguech newcharacterizationsofcompletelymonotonefunctionsandbernsteinfunctionsaconversetohausdorffsmomentcharacterizationtheorem
AT wissemjedidi newcharacterizationsofcompletelymonotonefunctionsandbernsteinfunctionsaconversetohausdorffsmomentcharacterizationtheorem
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