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Inequalities for positive-definite functions

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Abstract

Generalizations of the classical inequality

$${\left| {f\left( x \right) - f\left( y \right)} \right|^2} \leqslant 2f\left( 0 \right)\left\{ {f\left( 0 \right) - \operatorname{Re} f\left( {x - y} \right)} \right\}$$

for a positive-definite complex-valued function f on an Abelian group are obtained.

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Authors and Affiliations

  1. Faculty of Mathematics, Moscow State Pedagogical University, Moscow, Russia

    E. A. Gorin

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  1. E. A. Gorin
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Correspondence to E. A. Gorin.

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Translated from Funktsional′nyi Analiz i Ego Prilozheniya, Vol. 49, No. 4, pp. 76–78, 2015 Original Russian Text Copyright © by E. A. Gorin

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Gorin, E.A. Inequalities for positive-definite functions. Funct Anal Its Appl 49, 301–303 (2015). https://doi.org/10.1007/s10688-015-0118-8

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  • DOI: https://doi.org/10.1007/s10688-015-0118-8

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