Inequalities of M.G. Krein, Yu.V. Linnik and E.A. Gorin for positive definite functions

TL;DR

This paper explores and extends classical inequalities for positive definite functions, demonstrating how certain inequalities are interconnected and providing generalized versions.

Contribution

The paper introduces modifications and generalizations of inequalities by Krein, Linnik, and Gorin, and shows the derivation of Gorin's multipoint inequality from Krein's two-point inequality.

Findings

Generalized inequalities for positive definite functions are established.

Gorin's multipoint inequality is derived from Krein's two-point inequality.

The relationships among inequalities by Krein, Linnik, and Gorin are clarified.

Abstract

We investigate inequalities of M.G. Krein, Yu.V. Linnik and E.A. Gorin for positive definite functions. Modifications and generalizations of these inequalities are proved. We also prove that multipoint E.A. Gorin's inequality follows from two--point M.G. Krein's inequality.