Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity

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From Schoenberg Coefficients to Schoenberg Functions (2015, background): “See [23] and the survey in [5] for details.”
Energy statistics: A class of statistics based on distances (2013, unknown): “A function ϕ from Rd to the complex numbers is called conditionally negative definite if for all choices of zi,j ¼ xi−yj, i,j¼ 1,…,n, for all complex numbers c1,…,cn, and all natural numbers n we have ∑ n i ¼ 1 ∑ n j ¼ 1 cicjϕðzi,jÞ≤0 ð5:4Þ whenever c1þc2þ⋯þcn ¼ 0 (see e.g. Berg, 2008).”
The Dagum family of isotropic correlation functions (2007, methodology): “Keywords: Bernstein function; completely monotonic function; Dagum family; isotropy; logarithmically completely monotonic function; Stieltjes transform”