Uniform approximation of differentiation operators by bounded linear operators in the space \(L_r\). (English) Zbl 1474.41035

The aim of the authors is to study the problem on the best uniform approximation on the axis of the differentiation operator of order \(k\) on the class of functions with bounded derivative of order \(n\), \(0 < k < n\), by bounded linear operators in the space \(L_r\), \(1\leq r < \infty\).
This is a variant of the “Stechkin problem” on the best approximation of an unbounded linear operator by bounded linear operators on a class of elements of a Banach space.


41A35 Approximation by operators (in particular, by integral operators)
26D10 Inequalities involving derivatives and differential and integral operators
41A50 Best approximation, Chebyshev systems
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