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

Abstract

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.