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

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. 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.