Geodesic
On generalizations of M.~G.~Krein, E.~A.~Gorin and Yu.~V.~Linnik inequalities for positive definite functions for multipoint case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 263-270.

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

In the paper some generalizations are proved for well–known inequalities of M. G. Krein, E. A. Gorin and Yu. V. Linnik for positive definite functions for multipoint case. It is proved that multipoint inequality of E. A. Gorin is derived from two–point inequality of M. G. Krein for positive definite functions. Also generalizations are considered of Yu. V. Linnik inequality for characteristic functions in probability theory.
Keywords: M. G. Krein, E. A. Gorin and Yu. V. Linnik inequalities, positive definite functions, characteristic functions, Bochner's theorem. 
@article{SEMR_2019_16_a129,
     author = {A. B. Pevnyi and S. M. Sitnik},
     title = {On generalizations of {M.~G.~Krein,} {E.~A.~Gorin} and {Yu.~V.~Linnik} inequalities for positive definite functions for multipoint case},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {263--270},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a129/}
}
TY  - JOUR
AU  - A. B. Pevnyi
AU  - S. M. Sitnik
TI  - On generalizations of M.~G.~Krein, E.~A.~Gorin and Yu.~V.~Linnik inequalities for positive definite functions for multipoint case
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 263
EP  - 270
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a129/
LA  - ru
ID  - SEMR_2019_16_a129
ER  - 
%0 Journal Article
%A A. B. Pevnyi
%A S. M. Sitnik
%T On generalizations of M.~G.~Krein, E.~A.~Gorin and Yu.~V.~Linnik inequalities for positive definite functions for multipoint case
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 263-270
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a129/
%G ru
%F SEMR_2019_16_a129
A. B. Pevnyi; S. M. Sitnik. On generalizations of M.~G.~Krein, E.~A.~Gorin and Yu.~V.~Linnik inequalities for positive definite functions for multipoint case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 263-270. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a129/

[1] M. Mathias, “Über positive Fourier–Integrale”, Math. Zeit., 16:1 (1923), 103–125 | DOI | MR | Zbl

[2] J. Stewart, “Positive definite functions and generalizations, an historical survey”, Rocky Mountain Journal of Mathematics, 6:3 (1976), 409–434 | DOI | MR | Zbl

[3] R. Bhatia, Positive definite matrices, Princeton University Press, Princeton, 2007 | MR | Zbl

[4] E.A. Gorin, “Positive definite functions as an instrument of mathematical analysis”, J. Math. Sci., 197:4 (2014), 492–511 | DOI | MR | Zbl

[5] E.A. Gorin, S. Norvidas, “Universal symbols on locally compact abelian groups”, Functional Analysis and Its Applications, 47:1 (2013), 1–13 | DOI | MR | Zbl

[6] M.G. Krein, “O predstavlenii funktsij integralami Fur'e-Stil't'esa”, Uchenye zapiski Kujbyshevskogo pedinstituta, 7 (1943); М. Г. Крейн, Избранные труды, т. 1, Киев, 1993 | Zbl

[7] M. G. Krein, “Measurable Hermitian–positive functions”, Mathematical Notes, 23:1 (1978), 79–91 | DOI | MR

[8] Z. Sasvari, Multivariate characteristic and correlation functions, Walter De Gruyter Co, Berlin, 2013 | MR

[9] E. Lukacs, Characteristic functions, Griffin, London, 1970 | MR | Zbl

[10] B. Ramachandran, Advanced theory of characteristic functions, Series in probability and statistics, Statistical Pub. Society, Calcutta, 1967 | MR | Zbl

[11] Yu. V. Linnik, Decompositions of probability laws, Izdat. Leningrad. Univ., Leningrad, 1960 | MR | Zbl

[12] W. Feller, An introduction to probability theory and its applications, v. 2, Wiley, 1957 | MR | Zbl

[13] D.S. Mitrinović, P. M. Vasić, Analytic inequalities, Springer, 1970 | MR | Zbl

[14] N.M. Sedrakyan, A.M. Avoyan, Inequalities, Fizmatlit, M., 2002

[15] G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1952 | MR | Zbl

[16] E. A. Gorin, “Inequalities for positivedefinite functions”, Funct. Anal. Appl., 49:4 (2015), 301–303 | DOI | MR | Zbl