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Optimal Recovery of the Derivative of Periodic Analytic Functions from Hardy Classes
Authors:Konstantin Yu Osipenko
Institution:Department of Mathematics, MATI—Russian State University of Technology, Petrovka 27, Moscow, 103767, Russia
Abstract:LetSβcolon, equals{zset membership, variantImage : |Im z|<β}. For 2π-periodic functions which are analytic inSβwithp-integrable boundary values, we construct an optimal method of recovery off′(ξ), ξset membership, variantSβ, using information about the valuesf(x1), mldr;, f(xn), xjset membership, variant0, 2π).
Keywords:
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