Relationship between the Hadamard Theorem on Three Disks and Certain Problems of Polynomial Approximation of Analytic Functions

• Date: 2001
• Main Authors: Vakarchuk, S. B., Вакарчук, С. Б.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4241
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

By using the classical Hadamard theorem, we obtain an exact (in a certain sense) inequality for the best polynomial approximations of an analytic function f(z) from the Hardy space H p, p ≥ 1, in disks of radii ρ, ρ1, and ρ2, 0 < ρ1 < ρ < ρ2 < 1.