Asymptotics of sharp constants in Markov–Bernstein–Nikolskii type inequalities with exponential weights

Abstract

We prove that the sharp constant in the univariate Bernstein–Nikolskii inequality for entire functions of exponential type is the limit of the sharp constant in the V. A. Markov type inequality with an exponential weight for coefficients of an algebraic polynomials of degree n as n→∞.