On the best approximation of the differentiation operator. (English) Zbl 1396.41018
Summary: In this paper we give a solution of the problem of the best approximation in the uniform norm of the differentiation operator of order \(k\) by bounded linear operators in the class of functions with the property that the Fourier transforms of their derivatives of order \(n(t<k<n)\) are finite measures. We also determine the exact value of the best constant in the corresponding inequality for derivatives.
MSC:
| 41A35 | Approximation by operators (in particular, by integral operators) |
| 41A50 | Best approximation, Chebyshev systems |
References:
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