Geodesic
Inequalities for Positive Definite Functions
Matematičeskie zametki, Tome 108 (2020) no. 6, pp. 823-836.

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Positive definite kernels and functions are considered. The key tool in the paper is the well-known main inequality for such kernels, namely, the Cauchy–Bunyakovskii inequality for the special inner product generated by a given positive definite kernel. It is shown that Ingham's inequality (and, in particular, Hilbert's inequality) is, essentially, the main inequality for the positive definite function $\sin(\pi x)/x$ on $\mathbb{R}$ and for a system of integer points. Using the main inequality, we prove new inequalities of Krein–Gorin type and Ingham's inequality.
Keywords: positive definite kernels and functions, Ingham's inequality, Hilbert's inequality, Krein's inequality, Weil's inequality, Gorin's inequality. 
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V. P. Zastavnyi. Inequalities for Positive Definite Functions. Matematičeskie zametki, Tome 108 (2020) no. 6, pp. 823-836. http://geodesic.mathdoc.fr/item/MZM_2020_108_6_a1/

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