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EXTREME VALUES OF FUNCTIONALS AND BEST APPROXIMATION ON CLASSES OF PERIODIC FUNCTIONS
In this paper, we compute upper bounds for the best approximation by trigonometric polynomials in the metrics and on the classes of 2-periodic functions such that , where is a given convex modulus ofExpand
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BEST QUADRATURE FORMULAS FOR CLASSES OF DIFFERENTIABLE FUNCTIONS AND PIECEWISE-POLYNOMIAL APPROXIMATION
In this article we obtain characteristic properties of piecewise-polynomial functions (spline functions) that have least deviation from zero in the metric of C. This has allowed us to obtainExpand
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INEQUALITIES FOR DIFFERENTIABLE PERIODIC FUNCTIONS AND BEST APPROXIMATION OF ONE CLASS OF FUNCTIONS BY ANOTHER
New results are obtained in this paper which elucidate properties of differentiable periodic functions connected with rearrangements. These results are applied in order to obtain a sharp estimate ofExpand
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On approximation of a class by another class and extremal subspaces inL1
AbstractПолучена оценка (в опр еделенном смысле неу лучшаемая) наилучшего приближе ния в метрикеL1=L1(0,2π) 2π-перио дических функций кла сса WrHω = {f:f∈Cr,ω(f(r),δ) ≦ ω(δ)}, r = 0, 1, ..., (ω(δ) —Expand
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On extremal subspaces and approximation of periodic functions by splines of minimal defect
AbstractН. П. Корнейчук СССР, ДНЕПРОПЕТРОВСК 320 625 ПР. ГАГАРИНА 72 ДНЕПРОПЕТРОВСКИЙ ГО СУДАРСТВЕННЫЙ УНИВЕ РСИТЕТ
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WIDTHS IN $ L_p$ OF CLASSES OF CONTINUOUS AND OF DIFFERENTIABLE FUNCTIONS, AND OPTIMAL METHODS OF CODING AND RECOVERING FUNCTIONS AND THEIR DERIVATIVES
Exact values of linear widths (diameters), Kolmogorov widths and Gel'fand widths, in -spaces are found for some classes of functions, using a convex majorant of the modulus of continuity of aExpand
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