Lower bound in the Bernstein inequality for the first derivative of algebraic polynomials

• Datum: 2009
• Hauptverfasser: Podvysotskaya, A. I., Подвысоцкая, А. И.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2009
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3053
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove that $\max |p′(x)|$, where $p$ runs over the set of all algebraic polynomials of degree not higher than $n ≥ 3$ bounded in modulus by 1 on [−1, 1], is not lower than \( {{\left( {n - 1} \right)} \mathord{\left/{\vphantom {{\left( {n - 1} \right)} {\sqrt {1 - {x^2}} }}} \right.} {\sqrt {1 -...