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Chebyshev constants for the unit circle
It is proven that for any system of n points z_1, ..., z_n on the (complex)
unit circle, there exists another point z of norm 1, such that
Equality holds iff the point system is a
rotated copy of the nth unit roots.
Two proofs are presented: one uses a characterisation of equioscillating
rational functions, while the other is based on Bernstein's inequality.Comment: 11 page
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