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Research Article | Open Access

Classes of completely monotone and Bernstein functions defined by convexity properties of their spectral measures

Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia; wjedidi@ksu.edu.sa
Department of Statistical and Actuarial Sciences, Western University, 1151 Richmond Str., London, ON, N6A 5B7 Canada; hsendov@uwo.ca
Department of Statistical and Actuarial Sciences, Western University, 1151 Richmond Str., London, ON, N6A 5B7 Canada; sshan2@uwo.ca
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Abstract

We were interested in Bernstein and Lévy measures having certain convexity-type properties. The convexity-type properties were an extension of the harmonic convexity property considered in [9]. We characterized the corresponding completely monotone and Bernstein functions. We hope this paper can aid with understanding the analogous properties and open questions presented in [8,9].

Keywords

completely monotone functionBernstein functionβ-convexβ-concave tailharmonic convexity
CLC number: 26A48, 26D07

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 11372-11395
DOI: 10.3934/math.2024558

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Cite this article:
Jedidi W, Sendov HS, Shan S. Classes of completely monotone and Bernstein functions defined by convexity properties of their spectral measures. AIMS Mathematics, 2024, 9(5): 11372-11395. https://doi.org/10.3934/math.2024558

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Received: 31 December 2023
Revised: 07 March 2024
Accepted: 15 March 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)