Asymptotics of Sharp Constants in Markov-Bernstein-Nikolskii type Inequalities with Exponential Weights

TL;DR

This paper establishes the asymptotic behavior of sharp constants in Bernstein-Nikolskii inequalities with exponential weights, linking them to Markov-type inequalities for polynomial coefficients as degree increases.

Contribution

It provides a new asymptotic relation between sharp constants in Bernstein-Nikolskii and Markov inequalities involving exponential weights for entire functions.

Findings

Sharp constants in Bernstein-Nikolskii inequalities converge to those in Markov inequalities.

Asymptotic limits are characterized for exponential weights.

Results enhance understanding of polynomial 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 $n\to\iy$.