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arXiv · 1706.00669

Lower estimates for linear operators with smooth range

Johannes Nagler
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Abstract

We introduce a new method to prove lower estimates for the approximation error of general linear operators with smooth range in terms of classical moduli of smoothness and related $K$-functionals. In addition, we explicitly show how to derive lower estimates for positive linear operators with smooth range and apply this result to classical approximation operators. We finish with some remarks on the eigenvalues of Schoenberg's spline operator.

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Johannes Nagler. 2017-06-02. Lower estimates for linear operators with smooth range. https://arxiv.org/abs/1706.00669

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