指数型全函数小于整数阶的里兹衍的伯恩斯坦不等式

Pub Date : 2024-03-14 DOI:10.1134/S1064562423701491

A. O. Leont’eva

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摘要

Abstract We consider Bernstein inequality for the Riesz derivative of order \(0 < \alpha < 1\) of entire function of exponential type in the uniform norm on the real line.可以得到这个算子的插值公式；这个公式有非等距节点。通过这个公式，找到了所有 \(0 < \alpha < 1\) 的精确伯恩斯坦不等式，即写出了极值整个函数和锐常数。

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Bernstein Inequality for the Riesz Derivative of Fractional Order Less Than Unity of Entire Functions of Exponential Type

We consider Bernstein inequality for the Riesz derivative of order \(0 < \alpha < 1\) of entire function of exponential type in the uniform norm on the real line. The interpolation formula is obtained for this operator; this formula has non-equidistant nodes. By means of this formula, the exact Bernstein inequality is found for all \(0 < \alpha < 1\), namely, the extremal entire function and the sharp constant are written out.

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