Geodesic
Bernstein Inequality for the Riesz Derivative of Order $0\alpha1$ of Entire Functions of Exponential Type in the Uniform Norm
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 245-256

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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.
Keywords: entire functions of exponential type, Riesz derivative, Bernstein inequality, uniform norm, Bessel function. 
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     author = {A. O. Leont'eva},
     title = {Bernstein {Inequality} for the {Riesz} {Derivative} of {Order} $0<\alpha<1$ of {Entire} {Functions} of {Exponential} {Type} in the {Uniform} {Norm}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {245--256},
     publisher = {mathdoc},
     volume = {115},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a7/}
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A. O. Leont'eva. Bernstein Inequality for the Riesz Derivative of Order $0<\alpha<1$ of Entire Functions of Exponential Type in the Uniform Norm. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 245-256. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a7/