BEST LINEAR METHODS OF APPROXIMATION OF FUNCTIONS OF THE HARDY CLASS Hp


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Abstract

We determine the exact value of the best linear polynomial approximation of a unit ball of the Hardy space Hp, 1 ≤ p ≤ ∞, on concentric circles Tρ = {z ε C: |z| = |ρ|}, 0 ≤ ρ < 1, in the uniform metric. We construct the best linear method of approximation and prove the uniqueness of this method.

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