# A Lower Bound for the Minimum Deviation of the Chebyshev Polynomial on a Compact Real Set

```@inproceedings{Schiefermayr2008ALB,
title={A Lower Bound for the Minimum Deviation of the Chebyshev Polynomial on a Compact Real Set},
author={Klaus Schiefermayr},
year={2008}
}```
In this paper, we give a sharp lower bound for the minimum deviation of the Chebyshev polynomial on a compact subset of the real line in terms of the corresponding logarithmic capacity. Especially if the set is the union of several real intervals, together with a lower bound for the logarithmic capacity derived recently by A.Yu. Solynin, one has a lower bound for the minimum deviation in terms of elementary functions of the endpoints of the intervals. In addition, analogous results for compact… CONTINUE READING

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## Transfinite diameter

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