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Exact Constants in Approximation Theory
Preface 1. Best approximation and duality in extremal problems 2. Polynomials and spline-functions as approximating tools 3. Comparison theorems and inequalities for the norms of functions and theirExpand
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ON METHODS OF INVESTIGATING EXTREMAL PROBLEMS IN THE THEORY OF BEST APPROXIMATION
This article is of the nature of a survey. It sets out the basic steps of the investigations into the exact solution of extremal problems in the theory of approximation for classes of periodicExpand
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Kolmogorov-type inequalities for mixed derivatives of functions of many variables
AbstractLet γ = (γ1 ,..., γd ) be a vector with positive components and let Dγ be the corresponding mixed derivative (of order γj with respect to the j th variable). In the case where d > 1 and 0 < kExpand
S. M. Nikol'skii and the development of research on approximation theory in the USSR
CONTENTSIntroduction § 1. Duality relations and extremal problems of approximation theory § 2. Approximation of classes of functions defined by a modulus of continuity § 3. Approximation of functionsExpand
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