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

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 function
• bernstein function
• $ \beta $-convex
• $ \beta $-concave tail
• harmonic convexity