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Journal of Convex Analysis 23 (2016), No. 4, 981--1015
Copyright Heldermann Verlag 2016



Properties of Completely Monotone and Bernstein Functions Related to the Shape of Their Measures

Hristo Sendov
Dept. of Statistical and Actuarial Sciences, Western University, 1151 Richmond Str., London, Ont., Canada N6A 5B7
hssendov@stats.uwo.ca

Shen Shan
Dept. of Statistical and Actuarial Sciences, Western University, 1151 Richmond Str., London, Ont., Canada N6A 5B7
sshan2@uwo.ca



We are interested in Bernstein and LÚvy measures having certain convexity-type properties. We thoroughly investigate how the shape of these measures results in various properties of the corresponding completely monotone and Bernstein functions. We hope that by understanding these connections one would be able to shed more light on the several conjectures posed in another paper of the authors ["New representation theorems for completely monotone and Bernstein functions with convexity properties on their measures", J. Theoretical Probability (2014), DOI 10.1007/s10959-014-0557-9].

Keywords: Bernstein function, completely monotone function, Bernstein measure, LÚvy measure, harmonically convex function.

MSC: 26A48, 26D07; 30E20

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