Bernstein Inequality for the Riesz Derivative of Order $$0<\alpha<1$$ of Entire Functions of Exponential Type in the Uniform Norm

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s000143462401019x

A. O. Leont’eva

引用次数: 0

Abstract

We consider Bernstein’s inequality for the Riesz derivative of order $0<\alpha<1$ of entire functions of exponential type in the uniform norm on the real line. For this operator, the corresponding interpolation formula is obtained; this formula has nonequidistant nodes. Using this formula, the sharp Bernstein inequality is obtained for all $0<\alpha<1$; namely, the extremal entire function and the sharp constant are written out.

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统一规范中指数型全函数的 $$0<\alpha<1$$ 阶里兹衍生物的伯恩斯坦不等式

摘要我们考虑了实线上指数型全函数的阶 $0<\alpha<1)里兹导数的伯恩斯坦不等式。对于这个算子，可以得到相应的插值公式；这个公式具有非等价节点。利用这个公式，可以得到所有 \(0<\alpha<1$的尖锐伯恩斯坦不等式；即写出极值整个函数和尖锐常数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.