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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 263–270 (Mi semr1060)  

Real, complex and functional analysis

On generalizations of M. G. Krein, E. A. Gorin and Yu. V. Linnik inequalities for positive definite functions for multipoint case

A. B. Pevnyia, S. M. Sitnikb

a Syktyvkar State University, 55, October ave., Syktyvkar, 167001, Russia
b Belgorod State National Research University, 85, Pobeda str., Belgorod, 308015, Russia

Abstract: 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.

DOI: https://doi.org/10.33048/semi.2019.16.018

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Bibliographic databases:

Document Type: Article
UDC: 517.518.28
MSC: 42A82
Received March 6, 2018, published March 5, 2019

Citation: 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”, Sib. Èlektron. Mat. Izv., 16 (2019), 263–270

Citation in format AMSBIB
\Bibitem{PevSit19}
\by A.~B.~Pevnyi, S.~M.~Sitnik
\paper On generalizations of M.~G.~Krein, E.~A.~Gorin and Yu.~V.~Linnik inequalities for positive definite functions for multipoint case
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 263--270
\mathnet{http://mi.mathnet.ru/semr1060}
\crossref{https://doi.org/10.33048/semi.2019.16.018}


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