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arXiv · 1009.4430

Bernstein type inequality in monotone rational approximation

Andriy V. Bondarenko·Maryna S. Viazovska
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Abstract

The following analog of Bernstein inequality for monotone rational functions is established: if $R$ is an increasing on $[-1,1]$ rational function of degree $n$, then $$ R'(x)<\frac{9^n}{1-x^2}\|R\|,\quad x\in (-1,1). $$ The exponential dependence of constant factor on $n$ is shown, with sharp estimates for odd rational functions.

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Andriy V. Bondarenko, Maryna S. Viazovska. 2010-09-22. Bernstein type inequality in monotone rational approximation. https://arxiv.org/abs/1009.4430

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