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arXiv · 1312.5546

A lower bound for the uniform Schoenberg operator

Johannes Nagler·Uwe Kähler
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Abstract

We present an estimate for the lower bound for the Schoenberg operator with equidistant knots in terms of the second order modulus of smoothness. We investigate the behaviour of iterates of the Schoenberg operator and in addition, we show an upper bound of the second order derivative of these iterates. Finally, we prove the equivalence between the approximation error and the second order modulus of smoothness.

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Johannes Nagler, Uwe Kähler. 2013-12-19. A lower bound for the uniform Schoenberg operator. https://arxiv.org/abs/1312.5546

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