Geodesic
On the Positive Definiteness of Some Functions Related to the Schoenberg Problem
Matematičeskie zametki, Tome 102 (2017) no. 3, pp. 355-368.

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For a broad class of functions $f\colon[0,+\infty)\to\mathbb{R}$, we prove that the function $f(\rho^{\lambda}(x))$ is positive definite on a nontrivial real linear space $E$ if and only if $0\le\lambda\le \alpha(E,\rho)$. Here $\rho$ is a nonnegative homogeneous function on $E$ such that $\rho(x)\not\equiv 0$ and $\alpha(E,\rho)$ is the Schoenberg constant.
Keywords: positive definite function, completely monotone function, Schoenberg problem, Kuttner–Golubov problem, Bochner theorem.
Mots-clés : Fourier transform 
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V. P. Zastavnyi; A. D. Manov. On the Positive Definiteness of Some Functions Related to the Schoenberg Problem. Matematičeskie zametki, Tome 102 (2017) no. 3, pp. 355-368. http://geodesic.mathdoc.fr/item/MZM_2017_102_3_a2/

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