Geodesic
Inequalities for Positive-Definite Functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 4, pp. 76-78

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Generalizations of the classical inequality $|f(x)-f(y)|^2\le2f(0)\{f(0)-\operatorname{Re}f(x-y)\}$ for a positive-definite complex-valued function $f$ on an Abelian group are obtained.
Keywords: positive-definite function on an Abelian group, Bochner's theorem. 
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     author = {E. A. Gorin},
     title = {Inequalities for {Positive-Definite} {Functions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_4_a5/}
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E. A. Gorin. Inequalities for Positive-Definite Functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 4, pp. 76-78. http://geodesic.mathdoc.fr/item/FAA_2015_49_4_a5/