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An extremal property of Chebyshev polynomials
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March 11, 2008
It is proved that if f (x) is a polynomial of the degree not exceeding n with real coefficients, which satisfies the condition |f (x)| ≤ 1 for all x ∈ [–1,1], then the sum of the absolute values of its coefficients attains its maximal value at f (x) = Tn(x) = cos (n arccos x).
Published Online: 2008-03-11
Published in Print: 2008-01
© de Gruyter 2008
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