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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 514, Number 1, Pages 118–122
DOI: https://doi.org/10.31857/S2686954323600611 (Mi danma442) 		 
MATHEMATICS

Bernstein inequality for Riesz derivative of fractional order less than 1 of entire function of exponential type

A. O. Leont'eva

Ural Federal University, Yekaterinburg, Russian Federation
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DOI: https://doi.org/10.31857/S2686954323600611
Abstract: We consider Bernstein inequality for the Riesz derivative of order 0$<\alpha<$1 of entire functions of exponential type in the uniform norm on the real line. The interpolation formula for this operator is obtained; this formula has non-equidistant nodes. By means of this formula, the sharp Bernstein inequality is obtained for all 0$<\alpha<$1, more precisely, the extremal entire function and the exact constant are written out.
Keywords: entire functions of exponential type, Riesz derivative, Bernstein inequality, uniform norm, bessel functions.
Funding agency Grant number
Russian Science Foundation 22-21-00526
The research is supported by Russian Science Foundation (project no. 22-21-00526, https://rscf.ru/en/project/22-21-00526/) in the Ural Federal University.
Presented: V. I. Berdyshev
Received: 01.07.2023
Revised: 10.10.2023
Accepted: 03.11.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 3, Pages 524–527
DOI: https://doi.org/10.1134/S1064562423701491
Bibliographic databases:
Document Type: Article
UDC: 517.518.86
Language: Russian
Citation: A. O. Leont'eva, “Bernstein inequality for Riesz derivative of fractional order less than 1 of entire function of exponential type”, Dokl. RAN. Math. Inf. Proc. Upr., 514:1 (2023), 118–122; Dokl. Math., 108:3 (2023), 524–527
Citation in format AMSBIB
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\by A.~O.~Leont'eva
\paper Bernstein inequality for Riesz derivative of fractional order less than 1 of entire function of exponential type
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 514
\issue 1
\pages 118--122
\mathnet{http://mi.mathnet.ru/danma442}
\crossref{https://doi.org/10.31857/S2686954323600611}
\elib{https://elibrary.ru/item.asp?id=56718090}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 3
\pages 524--527
\crossref{https://doi.org/10.1134/S1064562423701491}
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