Bernstein Inequality for the Riesz Derivative of Order $0\alpha1$ of Entire Functions of Exponential Type in the Uniform Norm

A. O. Leont'eva

Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 245-256.

Résumé

We consider Bernstein's inequality for the Riesz derivative of order $0\alpha1$ 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 $0\alpha1$; namely, the extremal entire function and the sharp constant are written out.

Détail

Keywords: entire functions of exponential type, Riesz derivative, Bernstein inequality, uniform norm, Bessel function.

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