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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2020_108_6_a1,
     author = {V. P. Zastavnyi},
     title = {Inequalities for {Positive} {Definite} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {823--836},
     publisher = {mathdoc},
     volume = {108},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_6_a1/}
}
TY  - JOUR
AU  - V. P. Zastavnyi
TI  - Inequalities for Positive Definite Functions
JO  - Matematičeskie zametki
PY  - 2020
SP  - 823
EP  - 836
VL  - 108
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_108_6_a1/
LA  - ru
ID  - MZM_2020_108_6_a1
ER  - 
%0 Journal Article
%A V. P. Zastavnyi
%T Inequalities for Positive Definite Functions
%J Matematičeskie zametki
%D 2020
%P 823-836
%V 108
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_108_6_a1/
%G ru
%F MZM_2020_108_6_a1
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/